# Aptitude Questions: Mixtures And Alligations Set 7

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 !!

1. 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                                3/4
.                  7/10
3/4 – 7/10               7/10 – 2/5
1/20 : 3/10
1 : 6
So in 3rd mixture, 2nd mixture is [6/(1+6)] * 7 = 6 litres

2. 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)                2nd wheat (8 kg)
8                                                12
.                             9.6
12-9.6                                        9.6-8
2.4 1.6
3 : 2
So x/8 = 3/2

3. 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 – 15/x]2
So x [1 – 15/x]2 / x = 16/16+9
[1 – 15/x]2 = 16/25
Square root both sides, so [1 – 15/x] = 4/5
Solve, x = 75

4. 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                              x
.                 42
x-42                     42-36=6
so x-42/6 = 1/1
solve, x = 48

5. 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

6. 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

7. 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)                        Pure milk (x litres)
80                                                  100
.                             85
15                                                        5
3 : 1
So 75/x = 3/1
Solve, x = 25

8. 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                         -15
.                10
10-(-15)                 20-10
25 : 10
5 : 2
So at 20% profit = 5/(5+2) * 560

9. 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                          18
.             15
3                           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

10. 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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