Mixture and Alligation — Extra Practice

Competitive Mathematics · Arithmetic

6 Part15 worked examples100 practice questions

NoteThis is the Extra Practice set: lots of questions. To learn the methods first, read the main chapter of the same topic (the one without “Extra Practice” in its name), then practise here.

A tea shop blends leaf at ₹300 a kg with leaf at ₹500 a kg to make a ₹400 blend. The question: in what ratio? Here the answer is obvious — equal. But what if the blend must be ₹420? This is where alligation helps: a small cross-subtraction table that gives the ratio without writing equations. Its magic is that it works on anything “per unit” — price, per cent, speed, average, profit.

∑ Formula

\frac{सस्ते की मात्रा}{महँगे की मात्रा} = \frac{d - m}{m - c}

The alligation formula (

c

cheaper,

d

dearer,

m

mean)

Mean price and alligation

Cross subtraction

The mean price of a blend and the ratio in which cheap and dear are mixed.

Mean price

Always between the two prices

The cost per unit of the blend — total cost ÷ total quantity.

The mean price of a blend is dearer than the cheap item and cheaper than the dear one. It is the weighted mean from the average chapter: $mean price = \frac{q _{1} p _{1} + q _{2} p _{2}}{q _{1} + q _{2}}$ . The more of an item, the closer the mean to its price.

Example 1 · Basic

20 kg of tea at ₹300/kg and 30 kg at ₹400/kg are blended. What is the mean price?

Solution, step by step

1Total cost $= 6000 + 12000 = 18000$ ; total quantity $= 50$ .
2Mean $= \frac{18000}{50} = 360$

Answer ₹360

BasicTry it yourself first

Tea of 10 kg at ₹40/kg, 30 kg at ₹60/kg is blended. What is the mean price per kg of the blend?

StandardTry it yourself first

Tea of 24 kg at ₹35/kg, 16 kg at ₹55/kg, 20 kg at ₹60/kg is blended. What is the mean price per kg of the blend?

AdvancedTry it yourself first

Tea of 35 kg at ₹48/kg, 25 kg at ₹72/kg, 40 kg at ₹60/kg is blended. What is the mean price per kg of the blend?

StandardTry it yourself first

20 kg of sugar at ₹24/kg and 30 kg at ₹32/kg are mixed and the blend sold at ₹33/kg. What is the gain or loss per cent?

AdvancedTry it yourself first

40 kg of sugar at ₹36/kg and 60 kg at ₹46/kg are mixed and the blend sold at ₹48/kg. What is the gain or loss per cent?

The alligation method

Cheaper : dearer

= (d - m) : (m - c)

Three prices, one ratio — and the quantity when the total is given.

Method: write the cheaper price $c$ and the dearer price $d$ , with the target mean $m$ in the middle. Subtract crosswise: $d - m$ gives the cheaper item’s share and $m - c$ the dearer’s. The ratio always puts more of the item whose price is nearer the mean.

CheckCheck: to make a ₹440 blend from ₹400 and ₹500, 440 is nearer ₹400, so more of the ₹400 item goes in. The ratio

(500 - 440) : (440 - 400) = 60 : 40 = 3 : 2

shows exactly that.

Example 2 · Basic

In what ratio must rice at ₹45/kg and ₹60/kg be mixed to get ₹48/kg?

Solution, step by step

1Cheaper’s share $= 60 - 48 = 12$ ; dearer’s $= 48 - 45 = 3$ .
2Ratio $12 : 3 = 4 : 1$

Answer 4 : 1

Example 3 · Standard

Two varieties of rice at ₹36 and ₹52/kg are mixed to make 80 kg worth ₹46/kg. How many kg of each?

Solution, step by step

1Ratio $= (52 - 46) : (46 - 36) = 6 : 10 = 3 : 5$ .
2Cheaper $= 80 \times \frac{3}{8} = 30$ kg; dearer $= 50$ kg

Answer 30 kg and 50 kg

Example 4 · Advanced

Two varieties at ₹50 and ₹80 per kg are mixed and sold at ₹68.40 per kg, giving a 14% profit. In what ratio were they mixed?

Solution, step by step

1The blend’s cost price $= \frac{68.4 \times 100}{114} = 60$ per kg.
2Cheaper : dearer $= (80 - 60) : (60 - 50) = 20 : 10 = 2 : 1$ .

Answer 2 : 1

First get the cost from the selling price, then alligate.

Example 5 · Standard

In what ratio must tea at ₹95/kg be blended with tea at ₹70/kg to get a blend worth ₹80/kg?

Solution, step by step

1Cheaper : dearer $= (95 - 80) : (80 - 70) = 15 : 10$ .
2 $= 3 : 2$

Answer 3 : 2

BasicTry it yourself first

In what ratio must rice at ₹30/kg and ₹50/kg be mixed to get a mixture worth ₹42/kg?

BasicTry it yourself first

In what ratio must rice at ₹24/kg and ₹40/kg be mixed to get a mixture worth ₹36/kg?

StandardTry it yourself first

In what ratio must rice at ₹18.5/kg and ₹24.5/kg be mixed to get a mixture worth ₹22/kg?

StandardTry it yourself first

In what ratio must rice at ₹64/kg and ₹96/kg be mixed to get a mixture worth ₹72/kg?

AdvancedTry it yourself first

In what ratio must rice at ₹275/kg and ₹425/kg be mixed to get a mixture worth ₹335/kg?

BasicTry it yourself first

Two varieties of rice at ₹30/kg and ₹50/kg are mixed to make 40 kg worth ₹42/kg. How many kg of the cheaper variety are used?

StandardTry it yourself first

Two varieties of rice at ₹36/kg and ₹52/kg are mixed to make 160 kg worth ₹46/kg. How many kg of the cheaper variety are used?

AdvancedTry it yourself first

Two varieties of rice at ₹120/kg and ₹180/kg are mixed to make 300 kg worth ₹150/kg. How many kg of the cheaper variety are used?

Alligation on per cents, profits and concentrations

Anything “per unit” in place of price

Alligation also works when the quantity is not a price but a per cent or a profit.

Concentrations of solutions

A per cent is also a price

The per cents of two solutions and their mixing ratio; adding the pure substance (100%) or water (0%).

Pure milk is 100% concentration and pure water 0%. To dilute a 20% salt solution add water (0%); to strengthen it add 100% salt. Alligation: lower% : higher% $= (high - target) : (target - low)$ .

Example 6 · Standard

In what ratio must 20% and 50% salt solutions be mixed to get a 35% solution?

Solution, step by step

1 $(50 - 35) : (35 - 20) = 15 : 15$ .
2Ratio $1 : 1$ — the target is exactly midway.

Answer 1 : 1

Example 7 · Standard

A 60-litre solution has 25% alcohol. How much pure alcohol must be added to make it 40%?

Solution, step by step

1Original (25%) : pure (100%) $= (100 - 40) : (40 - 25) = 60 : 15 = 4 : 1$ .
2 $\frac{60}{x} = \frac{4}{1}$ ⟹ $x = 15$ L

Answer 15 L

BasicTry it yourself first

In what ratio must solutions of 10% and 30% salt be mixed to get a 22% solution?

StandardTry it yourself first

In what ratio must solutions of 12% and 45% salt be mixed to get a 30% solution?

StandardTry it yourself first

In what ratio must solutions of 0% and 60% salt be mixed to get a 24% solution?

AdvancedTry it yourself first

In what ratio must solutions of 18% and 72% salt be mixed to get a 45% solution?

BasicTry it yourself first

A 70-litre solution has 40% milk. How much pure milk must be added so that milk becomes 60%?

StandardTry it yourself first

A 80-litre solution has 25% milk. How much pure milk must be added so that milk becomes 40%?

AdvancedTry it yourself first

A 120-litre solution has 35% milk. How much pure milk must be added so that milk becomes 50%?

Profit per cent and average speed

Selling parts at different profits

When part of the stock sells at one profit and the rest at another, the overall profit.

If part of a stock $Q$ sells at $p_{1} %$ profit and the rest at $p_{2} %$ with an overall profit of $p %$ , then the $p_{1}$ part : the $p_{2}$ part $= (p_{2} - p) : (p - p_{1})$ . The same rule works on speed (km/h) — for the distances / times of two legs.

Example 8 · Standard

A trader has 600 kg of rice. He sells part at a 10% profit and the rest at 25%, and overall gains 20%. How much was sold at 25%?

Solution, step by step

110% part : 25% part $= (25 - 20) : (20 - 10) = 5 : 10 = 1 : 2$ .
2The 25% part $= 600 \times \frac{2}{3} = 400$ kg

Answer 400 kg

Example 9 · Standard

A car covers the first 120 km at 40 km/h and the remaining 180 km at 60 km/h. What is the average speed?

Solution, step by step

1Time $= \frac{120}{40} + \frac{180}{60} = 3 + 3 = 6$ hours.
2Average speed $= \frac{300}{6} = 50$ km/h

Answer 50 km/h

BasicTry it yourself first

A trader has 400 kg of pulses. He sells part at a 10% profit and the rest at 20%, gaining 14% overall. How much was sold at 20%?

StandardTry it yourself first

A trader has 900 kg of pulses. He sells part at a 8% profit and the rest at 20%, gaining 17% overall. How much was sold at 20%?

StandardTry it yourself first

A trader has 750 kg of pulses. He sells part at a 12% profit and the rest at 27%, gaining 18% overall. How much was sold at 27%?

AdvancedTry it yourself first

A trader has 1240 kg of pulses. He sells part at a 6.5% profit and the rest at 22%, gaining 14.5% overall. How much was sold at 22%?

Draw-and-refill, ratio changes and vessels

Stories after the mixture is made

Repeated draw-off and refilling, ratio changes on adding water, pouring two vessels together and the dishonest milkman.

Repeated draw-and-refill

The fraction multiplies each time

Draw off $b$ litres from $a$ litres of pure liquid, refill with water, and repeat $k$ times.

∑ Formula

बचा शुद्ध द्रव = a (1 - \frac{b}{a})^{k}

After

k

operations

Each time the liquid drawn off is the same fraction of the mixture: the first time it is $\frac{b}{a}$ of pure milk, the second time the same fraction of the mixture (which now has less milk). So the milk is multiplied by $(1 - \frac{b}{a})$ each time; $b$ is not subtracted again and again.

Example 10 · Standard

A vessel has 50 L of milk. 10 L is drawn off and replaced by water, done twice. What is the final ratio of milk to water?

Solution, step by step

1Milk $= 50 \times (\frac{40}{50})^{2} = 50 \times 0.64 = 32$ L.
2Water $= 18$ ⟹ milk : water $= 32 : 18 = 16 : 9$

Answer 16 : 9

Example 11 · Advanced

A vessel holds 80 L of pure spirit. 20 L is drawn and replaced by water, done 3 times. How much spirit remains?

Solution, step by step

1The fraction left each time is $\frac{60}{80} = \frac{3}{4}$ .
2 $80 \times (\frac{3}{4})^{3} = 80 \times \frac{27}{64} = 33.75$ L

Answer 33.75 L

BasicTry it yourself first

A vessel holds 40 litres of milk. 8 litres are drawn off and replaced by water, and this is done 2 times in all. How much milk is in the vessel at the end?

StandardTry it yourself first

A vessel holds 60 litres of milk. 12 litres are drawn off and replaced by water, and this is done 2 times in all. How much water is in the vessel at the end?

StandardTry it yourself first

A vessel holds 125 litres of milk. 25 litres are drawn off and replaced by water, and this is done 3 times in all. How much milk is in the vessel at the end?

AdvancedTry it yourself first

A vessel holds 80 litres of milk. 16 litres are drawn off and replaced by water, and this is done 3 times in all. How much water is in the vessel at the end?

AdvancedTry it yourself first

A vessel holds 64 litres of milk. 16 litres are drawn off and replaced by water, and this is done 2 times in all. How much milk is in the vessel at the end?

Changing ratios and two vessels

Hold the unchanged item steady

Milk stays fixed when water is added; for two vessels add the real quantities.

When water is added: the milk stays; equalise the milk parts in the old and new ratios. The difference in water parts = the water added.
Pouring two vessels together: find the actual milk and water in each, add milk to milk and water to water, then take the ratio.
Dishonest milkman: if he adds water and sells at the milk price gaining $g %$ , water : milk $= g : 100$ .

Example 12 · Standard

A vessel has milk : water = 5 : 3. After 8 L of water is added the ratio is 5 : 4. How much is in the new mixture?

Solution, step by step

1Milk stays at 5 parts; water goes from 3 to 4 parts, so 1 part $= 8$ L.
2New total $= (5 + 4) \times 8 = 72$ L

Answer 72 L

Example 13 · Standard

A milkman adds water to milk and sells at the price of milk, gaining 20%. What is water : milk?

Solution, step by step

1Water : milk $= 20 : 100$ .
2 $= 1 : 5$

Answer 1 : 5

Example 14 · Advanced

Two vessels hold milk : water in the ratios 3 : 1 and 1 : 3. If equal quantities from both are mixed what is the new ratio?

Solution, step by step

1Take 4 L from each: milk $3 + 1 = 4$ , water $1 + 3 = 4$ .
2Ratio $= 4 : 4 = 1 : 1$

Answer 1 : 1

BasicTry it yourself first

In a vessel milk and water are in the ratio 3 : 2. After 8 litres of water are added the ratio becomes 3 : 3. How much water is in the new mixture?

StandardTry it yourself first

In a vessel milk and water are in the ratio 7 : 4. After 10 litres of water are added the ratio becomes 7 : 6. How much water is in the new mixture?

AdvancedTry it yourself first

In a vessel milk and water are in the ratio 9 : 5. After 18 litres of water are added the ratio becomes 9 : 8. How much water is in the new mixture?

BasicTry it yourself first

One vessel has 30 L of a milk : water mixture in the ratio 2 : 1, another has 40 L in the ratio 3 : 1. If both are poured into a big vessel what is milk : water?

StandardTry it yourself first

One vessel has 36 L of a milk : water mixture in the ratio 5 : 4, another has 45 L in the ratio 2 : 3. If both are poured into a big vessel what is milk : water?

AdvancedTry it yourself first

One vessel has 66 L of a milk : water mixture in the ratio 7 : 4, another has 70 L in the ratio 3 : 4. If both are poured into a big vessel what is milk : water?

BasicTry it yourself first

A milkman mixes water with milk and sells the mixture at the price of pure milk, gaining 25%. What is the ratio of water to milk?

StandardTry it yourself first

A milkman mixes water with milk and sells the mixture at the price of pure milk, gaining 12.5%. What is the ratio of water to milk?

AdvancedTry it yourself first

A milkman mixes water with milk and sells the mixture at the price of pure milk, gaining 16%. What is the ratio of water to milk?

Traps and fast tricks

Slips · tricks

Where marks go in mixtures.

The commonest mistakes

Six traps

The slips that cost marks.

Trap 1Crossing the subtraction the wrong way. The cheaper’s share is

d - m

, not

m - c

. Check: more of the item nearer the mean.

Trap 2Taking the plain mean of the prices. ₹50 is the mean of ₹40 and ₹60 only for equal quantities; otherwise a weighted mean.

Trap 3Subtracting $b$ again and again in draw-and-refill. Not

a - kb

but

a (1 - \frac{b}{a})^{k}

Trap 4Adding ratios directly. Pouring

2 : 1

and

3 : 1

vessels does not give

5 : 2

; add the real quantities.

Trap 5Alligating quantities instead of per-unit values. Alligation is on per-unit values (%, ₹/kg), not on totals.

Trap 6Changing both parts when water is added. The water parts change, not the milk’s.

Fast tricks

Checks and reverse working

Habits that raise your confidence in the answer.

Check: rebuild the mean from the ratio — $\frac{a c + b d}{a + b} = m$ must hold.
Simple ratios: multiply decimal prices by 100 (₹6.20 and ₹7.20 ⟹ 620 and 720).
With three items: pair a cheaper with a dearer; many answers are possible — match with the options.
Draw-and-refill: exams choose $\frac{b}{a}$ as a simple fraction (like $\frac{1}{5}$ ) so the multiplication is quick.
Hold the steady one: in every ratio change one item stays — equalise it.

Example 15 · Standard

Check: what is the price of a blend of ₹30 and ₹50 per kg mixed in the ratio 3 : 2?

Solution, step by step

1Price $= \frac{3 \times 30 + 2 \times 50}{3 + 2} = \frac{190}{5}$ .
2 $= 38$ — near the cheaper one, as it should be.

Answer ₹38

The practice ladder

Basic → standard → advanced

New questions of every type, in three levels.

Level 1 — Basic

Direct rules

One-rule questions.

BasicTry it yourself first

In what ratio must rice at ₹20/kg and ₹40/kg be mixed to get a mixture worth ₹28/kg?

BasicTry it yourself first

In what ratio must rice at ₹50/kg and ₹70/kg be mixed to get a mixture worth ₹62/kg?

BasicTry it yourself first

In what ratio must solutions of 15% and 35% salt be mixed to get a 30% solution?

BasicTry it yourself first

Two varieties of rice at ₹25/kg and ₹45/kg are mixed to make 60 kg worth ₹35/kg. How many kg of the cheaper variety are used?

BasicTry it yourself first

Two varieties of rice at ₹40/kg and ₹60/kg are mixed to make 100 kg worth ₹54/kg. How many kg of the cheaper variety are used?

BasicTry it yourself first

Tea of 20 kg at ₹30/kg, 30 kg at ₹40/kg is blended. What is the mean price per kg of the blend?

BasicTry it yourself first

Tea of 15 kg at ₹20/kg, 10 kg at ₹50/kg is blended. What is the mean price per kg of the blend?

BasicTry it yourself first

10 kg of sugar at ₹20/kg and 10 kg at ₹30/kg are mixed and the blend sold at ₹35/kg. What is the gain or loss per cent?

BasicTry it yourself first

A trader has 300 kg of pulses. He sells part at a 10% profit and the rest at 20%, gaining 12% overall. How much was sold at 20%?

BasicTry it yourself first

A 60-litre solution has 20% milk. How much pure milk must be added so that milk becomes 40%?

BasicTry it yourself first

A vessel holds 100 litres of milk. 20 litres are drawn off and replaced by water, and this is done 2 times in all. How much milk is in the vessel at the end?

BasicTry it yourself first

A vessel holds 36 litres of milk. 12 litres are drawn off and replaced by water, and this is done 2 times in all. How much water is in the vessel at the end?

BasicTry it yourself first

In a vessel milk and water are in the ratio 2 : 1. After 10 litres of water are added the ratio becomes 2 : 2. How much water is in the new mixture?

BasicTry it yourself first

One vessel has 24 L of a milk : water mixture in the ratio 1 : 1, another has 48 L in the ratio 2 : 1. If both are poured into a big vessel what is milk : water?

BasicTry it yourself first

A milkman mixes water with milk and sells the mixture at the price of pure milk, gaining 20%. What is the ratio of water to milk?

Level 2 — Standard

Two ideas combined

Exam-level questions.

StandardTry it yourself first

In what ratio must rice at ₹36.5/kg and ₹54.5/kg be mixed to get a mixture worth ₹42.5/kg?

StandardTry it yourself first

In what ratio must rice at ₹85/kg and ₹145/kg be mixed to get a mixture worth ₹115/kg?

StandardTry it yourself first

In what ratio must solutions of 8% and 36% salt be mixed to get a 22% solution?

StandardTry it yourself first

In what ratio must solutions of 4% and 60% salt be mixed to get a 18% solution?

StandardTry it yourself first

In what ratio must items of value 35 and 55 be mixed for a mean of 47?

StandardTry it yourself first

Two varieties of rice at ₹48/kg and ₹72/kg are mixed to make 120 kg worth ₹60/kg. How many kg of the cheaper variety are used?

StandardTry it yourself first

Two varieties of rice at ₹140/kg and ₹200/kg are mixed to make 250 kg worth ₹164/kg. How many kg of the cheaper variety are used?

StandardTry it yourself first

Two varieties of rice at ₹52/kg and ₹88/kg are mixed to make 180 kg worth ₹61/kg. How many kg of the cheaper variety are used?

StandardTry it yourself first

Tea of 18 kg at ₹32/kg, 24 kg at ₹45/kg, 30 kg at ₹56/kg is blended. What is the mean price per kg of the blend?

StandardTry it yourself first

Tea of 25 kg at ₹64/kg, 35 kg at ₹48/kg is blended. What is the mean price per kg of the blend?

StandardTry it yourself first

25 kg of sugar at ₹34/kg and 15 kg at ₹54/kg are mixed and the blend sold at ₹52/kg. What is the gain or loss per cent?

StandardTry it yourself first

30 kg of sugar at ₹44/kg and 20 kg at ₹66/kg are mixed and the blend sold at ₹54/kg. What is the gain or loss per cent?

StandardTry it yourself first

A trader has 480 kg of pulses. He sells part at a 12% profit and the rest at 28%, gaining 20% overall. How much was sold at 28%?

StandardTry it yourself first

A trader has 750 kg of pulses. He sells part at a 8% profit and the rest at 18%, gaining 14% overall. How much was sold at 18%?

StandardTry it yourself first

A 90-litre solution has 30% milk. How much pure milk must be added so that milk becomes 50%?

StandardTry it yourself first

A 150-litre solution has 28% milk. How much pure milk must be added so that milk becomes 40%?

StandardTry it yourself first

A vessel holds 90 litres of milk. 18 litres are drawn off and replaced by water, and this is done 2 times in all. How much milk is in the vessel at the end?

StandardTry it yourself first

A vessel holds 150 litres of milk. 30 litres are drawn off and replaced by water, and this is done 3 times in all. How much milk is in the vessel at the end?

StandardTry it yourself first

A vessel holds 72 litres of milk. 24 litres are drawn off and replaced by water, and this is done 2 times in all. How much water is in the vessel at the end?

StandardTry it yourself first

In a vessel milk and water are in the ratio 4 : 3. After 18 litres of water are added the ratio becomes 4 : 5. How much water is in the new mixture?

StandardTry it yourself first

In a vessel milk and water are in the ratio 8 : 5. After 8 litres of water are added the ratio becomes 8 : 7. How much water is in the new mixture?

StandardTry it yourself first

One vessel has 28 L of a milk : water mixture in the ratio 3 : 4, another has 36 L in the ratio 5 : 4. If both are poured into a big vessel what is milk : water?

StandardTry it yourself first

One vessel has 54 L of a milk : water mixture in the ratio 4 : 5, another has 60 L in the ratio 1 : 4. If both are poured into a big vessel what is milk : water?

StandardTry it yourself first

A milkman mixes water with milk and sells the mixture at the price of pure milk, gaining 28%. What is the ratio of water to milk?

StandardTry it yourself first

A milkman mixes water with milk and sells the mixture at the price of pure milk, gaining 40%. What is the ratio of water to milk?

Level 3 — Advanced

Many steps and clever thinking

Questions at the hard end of competitive exams.

AdvancedTry it yourself first

In what ratio must rice at ₹192.5/kg and ₹312.5/kg be mixed to get a mixture worth ₹252.5/kg?

AdvancedTry it yourself first

In what ratio must solutions of 7.5% and 42.5% salt be mixed to get a 20% solution?

AdvancedTry it yourself first

In what ratio must solutions of 14% and 82% salt be mixed to get a 36% solution?

AdvancedTry it yourself first

In what ratio must items of value 28 and 74 be mixed for a mean of 53?

AdvancedTry it yourself first

Two varieties of rice at ₹88/kg and ₹136/kg are mixed to make 330 kg worth ₹112/kg. How many kg of the cheaper variety are used?

AdvancedTry it yourself first

Two varieties of rice at ₹275/kg and ₹395/kg are mixed to make 1200 kg worth ₹335/kg. How many kg of the cheaper variety are used?

AdvancedTry it yourself first

Tea of 45 kg at ₹72/kg, 35 kg at ₹96/kg, 60 kg at ₹84/kg is blended. What is the mean price per kg of the blend?

AdvancedTry it yourself first

60 kg of sugar at ₹38/kg and 40 kg at ₹58/kg are mixed and the blend sold at ₹52/kg. What is the gain or loss per cent?

AdvancedTry it yourself first

75 kg of sugar at ₹52/kg and 25 kg at ₹76/kg are mixed and the blend sold at ₹66/kg. What is the gain or loss per cent?

AdvancedTry it yourself first

A trader has 1600 kg of pulses. He sells part at a 7.5% profit and the rest at 27.5%, gaining 18% overall. How much was sold at 27.5%?

AdvancedTry it yourself first

A trader has 2160 kg of pulses. He sells part at a 4% profit and the rest at 22%, gaining 15% overall. How much was sold at 22%?

AdvancedTry it yourself first

A 230-litre solution has 36% milk. How much pure milk must be added so that milk becomes 54%?

AdvancedTry it yourself first

A 180-litre solution has 42% milk. How much pure milk must be added so that milk becomes 70%?

AdvancedTry it yourself first

A vessel holds 128 litres of milk. 32 litres are drawn off and replaced by water, and this is done 3 times in all. How much milk is in the vessel at the end?

AdvancedTry it yourself first

A vessel holds 200 litres of milk. 40 litres are drawn off and replaced by water, and this is done 3 times in all. How much water is in the vessel at the end?

AdvancedTry it yourself first

A vessel holds 96 litres of milk. 24 litres are drawn off and replaced by water, and this is done 3 times in all. How much milk is in the vessel at the end?

AdvancedTry it yourself first

In a vessel milk and water are in the ratio 11 : 7. After 15 litres of water are added the ratio becomes 11 : 10. How much water is in the new mixture?

AdvancedTry it yourself first

In a vessel milk and water are in the ratio 13 : 9. After 12 litres of water are added the ratio becomes 13 : 12. How much water is in the new mixture?

AdvancedTry it yourself first

One vessel has 63 L of a milk : water mixture in the ratio 4 : 5, another has 77 L in the ratio 7 : 4. If both are poured into a big vessel what is milk : water?

AdvancedTry it yourself first

One vessel has 90 L of a milk : water mixture in the ratio 7 : 3, another has 66 L in the ratio 3 : 8. If both are poured into a big vessel what is milk : water?

AdvancedTry it yourself first

A milkman mixes water with milk and sells the mixture at the price of pure milk, gaining 37.5%. What is the ratio of water to milk?

AdvancedTry it yourself first

A milkman mixes water with milk and sells the mixture at the price of pure milk, gaining 66%. What is the ratio of water to milk?

Revision — formula cards

Flip each card and test yourself

Read the front, think, then flip.