Hello Aspirants. Welcome to Online Quantitative Aptitude section in AffairsCloud.com. Here we are given some** Mixture and Alligations** problems that is important for competitive exams. We have included Some questions that are repeatedly asked in exams !!

**A mixture contains milk and water in the ratio 2 : 3 and the other contains them in the ratio 3 : 1 respectively. What weight of 2nd mixture must be taken so as to make a third mixture 7 litres in weight with 70% milk?**

A) 1 litre

B) 4 litres

C) 6 litres

D) 10 litres

E) 9 litres**C) 6 litres**

Explanation:

70/100 = 7/10

Milk in first = 2/(2+3) = 2/5, milk in second = 3/(3+1) = 3/4

By method of allegation:

2/5 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 3/4

. Â Â Â Â Â Â Â Â Â 7/10

3/4 – 7/10 Â Â Â Â Â Â Â 7/10 â€“ 2/5

1/20 : 3/10

1 : 6

So in 3rd mixture, 2nd mixture is [6/(1+6)] * 7 = 6 litres**How many kg of wheat costing Rs 8 per kg must be mixed with 8 Kg of wheat costing Rs 12 per Kg, so that there may be gain of 20% by selling the mixture of Rs 11.52 per Kg?**

A) 9 kg

B) 17 kg

C) 15 kg

D) 12 kg

E) 14 kg**D) 12 kg**

Explanation:

With 20% gain and SP = 11.52, CP = (100/120)*11.52 = 9.6

By method of allegation:

1st wheat (x kg) Â Â Â Â Â Â Â Â 2nd wheat (8 kg)

8 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 12

. Â Â Â Â Â Â Â Â Â Â Â Â Â Â 9.6

12-9.6 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 9.6-8

2.4 1.6

3 : 2

So x/8 = 3/2**15 litres of the milk is drawn out of a jar and filled with water. This operation is performed 1 more times. If the ratio of the quantity of milk left in jar to that of water in jar is 16 : 9, what was the initial quantity of milk present in the jar?**

A) 60 litres

B) 55 litres

C) 80 litres

D) 85 litres

E) 75 litres**E) 75 litres**

Explanation:

Let initial quantity of milk = x litres

After two times, quantity of milk left in jar = x [1 â€“ 15/x]^{2}

So x [1 â€“ 15/x]^{2}/ x = 16/16+9

[1 â€“ 15/x]^{2}= 16/25

Square root both sides, so [1 â€“ 15/x] = 4/5

Solve, x = 75**Wheat worth Rs 30 per kg and Rs 42 per kg are mixed with a third variety of wheat in the ratio 1 : 1 : 2 respectively. The mixture is worth Rs 42 per kg. Find the price (per kg) of the third variety of wheat.**

A) Rs 58

B) Rs 48

C) Rs 62

D) Rs 50

E) None of these**B) Rs 48**

Explanation:

Since 1st and 2nd wheat mixed in equal ratio, their average price = (30+42)/2 = 72/2 = Rs 36

Let 3rd variety of wheat be Rs x per kg

So they are mixed as : (1+1) : 2 = 1 : 1

So

36 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â x

. Â Â Â Â Â Â Â Â 42

x-42 Â Â Â Â Â Â Â Â Â Â 42-36=6

so x-42/6 = 1/1

solve, x = 48**A mixture contains A and B in the ratio 5 : 9. 14 litres of this mixture is taken out and 14 litres of B is poured in. Now the ratio of A to B becomes 2 : 5. Find the amount of B originally present in the mixture.**

A) 25 litres

B) 45 litres

C) 55 litres

D) 40 litres

E) 35 litres**B) 45 litres**

Explanation:

Total = 5x+9x+14 = 14x+14

So 5x/9x+14 = 2/5

Solve, x = 4

So total = 14*4 + 14 = 70 litres

So B = 9/(5+9) * 70 = 45**A mixture contains A and B in the ratio 5 : 7. 24 litres of this mixture is taken out and 15 litres of A is poured in. Now the ratio of A to B becomes 10 : 7. Find the amount of B originally present in the mixture.**

A) 25 litres

B) 45 litres

C) 55 litres

D) 40 litres

E) 35 litres**E) 35 litres**

Explanation:

Total = 5x+7x+24 = 12x+24

So 5x+15/7x = 10/7

Solve, x = 3

So total = 12*3 + 24 = 60 litres

So B = 7/(5+7) * 60 = 35**Milk contains 20% water. What quantity of pure milk should be added to 75 litres of this milk to reduce the quantity of water to 15%?**

A) 25 litres

B) 30 litres

C) 18 litres

D) 10 litres

E) 22 litres**A) 25 litres**

Explanation:

To have final mixture with water 15% means, milk = (100-15) = 85%

Pure milk is 100% milk, and in 75 litres of milk there is 80% milk so

Milk (75 litres) Â Â Â Â Â Â Â Â Â Â Â Â Pure milk (x litres)

80 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 100

. Â Â Â Â Â Â Â Â Â Â Â Â Â Â 85

15 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 5

3 : 1

So 75/x = 3/1

Solve, x = 25**An article is bought for Rs 560. Some of the part is sold at 20% profit and remaining at 15% loss giving a total of 10% profit. Find the cost price of part sold at 20% profit.**

A) Rs 350

B) Rs 385

C) Rs 400

D) Rs 430

E) Rs 225**C) Rs 400**

Explanation:

20 Â Â Â Â Â Â Â Â Â Â Â Â -15

. Â Â Â Â Â Â Â Â 10

10-(-15) Â Â Â Â Â Â Â Â 20-10

25 : 10

5 : 2

So at 20% profit = 5/(5+2) * 560**A man travelled a distance of 75 km in 5 hours partly on foot at the rate of 6 km/hour and partly by scooter at 18 km/hour. Find the distance travelled by scooter?**

A) 56 km

B) 52.25 km

C) 48.5 km

D) 67.5 km

E) 56.25 km**D) 67.5 km**

Explanation:

Average speed = 75/5 = 15 km/hr

By method of allegation:

6 Â Â Â Â Â Â Â Â Â Â Â Â Â 18

. Â Â Â Â Â Â 15

3 Â Â Â Â Â Â Â Â Â Â Â Â Â 9

1 : 3

1 : 3 is the ratio of times.

So time by scooter = 3/(1+3) * 5 = 3.75 hrs

So distance by scooter = 3.75 * 18**A 50 litres mixture of milk and water contains 10% water. 10 litres of this mixture is replaced by 10 litres of milk. What is the percentage of water in the final mixture?**

A) 9%

B) 8%

C) 7%

D) 8.5%

E) 6.5%**B) 8%**

Explanation:

When 10 litres taken out, quantity of mixture left =50-10=40, so

milk left = 90/100 *40 = 36

And water left = (10/100)*40 = 4

now 10 litres of milk poured in, so there is no change in quantity of water, and total mixture again becomes 50l

so water now is 4/50 * 100 = 8%

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