# Mixed Quantitative Aptitude Questions Set 8

1. Seven men and three boys can together do four times as much work as one man and one boy can do. Find the ratio of working capacity of one man to one boy.
A) 3 : 1
B) 2 : 1
C) 3 : 2
D) 4 : 3
E) 4 : 1
Option A
Solution:

7 m + 3b = 4 (m + b )
Solve 3m = b
So m/b = 3/1
2. A work which can be completed by 24 men in 15 days, can also be completed by 30 women in 16 days. 10 men and 10 women start working and work for 16 days. How many more men are required to work to complete the remaining work in 1 day?
A) 80
B) 72
C) 75
D) 56
E) 68
Option D
Solution:

24 m in 15 days, so 10 m in 24*15/10 = 36 days
30 w in 16 days, so 10 w in 30*16/10 = 48 days
So in 16 days they together complete = (1/36 + 1/48) * 16 = 7/9 work
Remaining work = 2/9
Now 24 m complete 1 work in 15 days. Let x men complete 2/9 work in 1 day
So
M1*D1*W2 = M2*D2*W1
24*15*(2/9) = x*1*1
x = 80
So extra men = 80 – 24 = 56
3. There are two containers filled with milk and water mixture. Capacity of containers is 18 litres and 12 litres respectively. They contain 35% water and 25% water respectively. If equal quantities from both the containers is mixed, then what will be the percentage of water in final mixture?
A) 11%
B) 30%
C) 15%
D) 28%
E) 22%
Option B
Solution:

Since there is equal quantity, so the final ratio should be 1 : 1
35…………………25
…………..x
1………………….1
So (35 – x)/(x – 25) = 1
Solve, x = 30 l
OR
Let x litres from both is taken
So final is x+x = 2x litres
So % = (35% of x + 25% of x)/2x * 100 = 30%
4. A solution contains milk and water in the ratio 3 : 1. 16 litres of the solution is drawn and 11 litres of water is added. If the final ratio of milk to water in the solution is 3 : 2, find the initial quantity of the solution.
A) 65 l
B) 54 l
C) 45 l
D) 60 l
E) None of these
Option D
Solution:

Let total solution = 3x + x + 16 = 4x + 16
Now 12 l water added, so
3x/(x+12) = 3/2
Solve x = 11
So total initial solution = 4 * 11 + 16 = 60 l
OR
Initially milk and water is 3x and x respectively
16 litres withdrawn:
Remaining Milk = 3x – 3/4 * 16 = 3x – 12
Remaining Water = x – 1/4 * 16 = x – 4
Remaining Milk = 3x – 12
Remaining Water = x – 4 + 11 = x + 7
Now (3x – 12)/(x + 7) = 3/2
Solve, x = 15
So total initial solution is 3x + x= 4x = 4*15 = 60 l
5. A and B invested Rs 5850 and Rs 6840. After 3 months, A added Rs 1650 and B withdrew Rs 840. If after a year, a total of Rs 41,800 is gained, what is the difference in the shares in the profit?
A) Rs 1900
B) Rs 2600
C) Rs 2500
D) Rs 1200
E) Rs 1800
Option A
Solution:

A : B
5850* 3 + 7500*9 : 6840*3 + 6000*9
65*3 + 750 : 76*3 + 600
189 : 207
21 : 23
So difference = (23-21)/(21+23) * 41800 = Rs 1900
6. Ratio of age of A three years hence to age of B 5 years hence will be 4 : 5. C’s age 7 years ago is two-thirds of A’s age 9 years hence. Also, the average age of B and C is 26. Find the age of B.
A) 25.5%
B) 22.5%
C) 20.5%
D) 18.5%
E) 23.5%
Option B
Solution:

(A+3)/(B+5) = 4/5
(C – 7) = 2/3 * (A + 9)
B + C = 2*26 = 52
Solve the equations, B = 25
7. Out of his monthly salary, Suhana spent 25% for her shopping of which she spent 80% in her food items. From the remaining salary, she spent two-eleventh on repair of furniture. If she saves Rs 14,400, what is her annual salary?
A) Rs 5,34,000
B) Rs 4,80,000
C) Rs 4,46,000
D) Rs 3,25,000
E) Rs 3,84,000
Option E
Solution:

Let monthly salary of Suhana is x
25% in shopping so 25% of x = x/4 in shopping
of which 80% in food items so, in food items = 80% of x/4 = x/5
So remaining salary = x – (x/4 + x/5) = 11x/20
Spent 2/11 on repair of furniture, so 1 – 2/11 = 9/11 is saved
So 9/11 * (11x/20) = 14400
Solve, x = Rs 32,000
So annual salary = 12*32,000 = Rs 3,84,000
8. A rectangle has its length and breadth in the ratio 4 : 5. If the dimensions of the rectangle are each increased by 5 m and area of rectangle thus formed is 340 m2, then what is the perimeter of the original rectangle?
A) 43 m
B) 36 m
C) 51 m
D) 54 m
E) 63 m
Option D
Solution:

4x, 5x
(4x+5)(5x+5) = 290
20x2 + 45x + 25 = 340
20x2 + 45x + 25 = 340
20x2 + 45x – 315 = 0
4x2 + 9x – 63 = 0
4x2 – 12x + 21x – 63 = 0
Solve, x = 3
So old perimeter = 2*(4x+5x) = 18x = 18*3 = 54m
9. There are n students in a class whose average weight is x kg. If 2 more students having total weight 50 kg are also counted for average, the average gets increased by 1. If 3 more students having total weight 67 kg are also counted for average, then also the average gets increased by 1. Find the initial number of students in class.
A) 18
B) 17
C) 16
D) 15
E) 19
Option C
Solution:

Case 1:
n………………………….x
(n+2)…………………….(x+1)
So (x+1)*2 + n*1 = 50
2x + n = 48
Case 2:
n………………………….x
(n+3)…………………….(x+1)
So (x+1)*3 + n*1 = 67
3x + n = 64
Solve both equations, n= 16
10. The speed of boat is 11 km/hr and speed of stream is 6 km/hr. In how much time can the 85 km distance going downstream from point A to B and coming back can be completed?
A) 18 hrs
B) 22 hrs
C) 20 hrs
D) 10 hrs
E) 15 hrs