Numerical Ability

 There are two mixtures A and B containing water and milk. A contains 20% water and B contains 30% water. Some quantity is taken from A and double this quantity from B, they are mixed to form another mixture C. What is the percentage of milk in mixture C?

• Let x litres taken from mixture A, then 2x litres from mixture B. So ratio of milk to water in mixture C =
  80% of x + 70% of 2x : 20% of x + 30% of 2x
  = (80/100) + (140/100) : (20/100) + (60/100)
  = 11 : 4
  So % of milk = [11/(11+4)] * 100=73.33%

A committee of 4 members is to be made from 5 men and 5 women. What is the probability that the committee will contain more men than women?

Explanation:
Case 1: all 4 men, 0 woman
Prob. = ⁵C₄/ ¹⁰C₄ = 1/42
Case 2: 3 men, 1 woman
Prob. = ⁵C₃ * ⁵C₁ / ¹⁰C₄ = 5/21
Add both cases = 1/42 + 5/21 = 11/42

An article is sold at 20% loss. If both the CP and SP of article are increased by Rs 20 and Rs 100 respectively, there is a profit of 5%. What is the original cost price of the article?

Explanation:
CP = x, then SP = (80/100)*x = 4x/5
New CP = (x+20), new SP = (4x/5 + 100), profit% = 5
So (4x/5 + 100) = (105/100) * (x+20)
(4x/5 + 100) = (21/20) * (x+20)
20*100 – 20*21 = 21x – (4x/5)*20
20(100-21) = 5x
Solve, x = 316

3/5th of work is completed by 20 men in 10 days working 6 hours each day. Now the remaining work is to be completed by some number of women in 10 days working 8 hours each day. If 4 women do as much work as is done by 2 men in one day, find the number of women required to complete the remaining work?

Explanation:
4 w = 2m, so 1 m = 2w
Let x men have to complete remaining (2/5th) work in 10 days working 8 hrs each day. so
M1*D1*H1*W2 = M2*D2*H2*W1
20*10*6*(2/5) = x*10*8*(3/5)
Solve, x = 10 men
Since, 1 m = 2w, so 10 men = 20 women

Directions  Study the given line graph carefully and answer the questions that follow.
The pie chart below shows the percentage of cars which each company A, B, C, D, and E produces in a week out of total 22,000 cars produced.
The table shows the ratio cars produced by each of the companies in their Mumbaid Pune plants.

Companies	Ratio of the number of cars produced – Mumbai : Pune
A	6	5
B	7	4
C	7	3
D	4	1
E	3	2

Total cars produced by company A is what per cent more than total cars produced by company D?

1.   Explanation:
Total cars by A = (25/100) * 22,000 = 5500
Cars produced by D = (15/100) * 22,000 = 3300
So required % = (5500-3300)/3300 * 100=66.67%

What is the total number of cars produced by companies A, B, C, and E together in Pune?

Explanation:
By A in Pune = (5/11) * (25/100) * 22000 = 2500
By B in Pune = (4/11) * (20/100) * 22000 = 1600
By C in Pune = (3/10) * (12/100) * 22000 = 792
By E in Pune = (2/5) * (18/100) * 22000 = 1584
Add all=6476

Which of the following company produce 2nd lowest in number of cars in Pune?

By D in Pune = (1/5) * (15/100) * 22000 = 660

What is the difference between the number of cars produced by companies B and C in Mumbai?

Explanation:
From question 6: By B in Mumbai = (7/11) * (20/100) * 22000 = 2800
By C in Mumbai = (7/10) * (12/100) * 22000 = 1848
Difference = 2800-1848=952

How many cars did company B produce in Mumbai in a week?

Explanation:
[7/(7+4)] * (20/100) * 22,000 = 2800

In a family, age of father is three times the sum of ages of his 2 children Monu and Sonu. 5 years from now, the sum of ages of Monu and Sonu will be half the age of their father. What will be the total of their ages, 10 years from now?

1.   Explanation:
Let (Monu+Sonu)’s present age= x
Then father’s present age = 3x
After 5 years, (x+5+5) = 1/2 (3x+5) [Add 5 to monu’s and sonu’s age]
Solve, x = 15
Sum of present ages = x+3x = 4x = 60
So after 10 years, add 10 age to all of them = 60+10+10+10=90

A and B started a business by investing Rs 10,000 and Rs 12,000 respectively. After 4 months they withdrew their half money and after another 4 Months they again withdrew their half of money of previous investment. If at the end of year A got Rs 10,500 as share of his profit, then what is the total profit made at the end of year?

Explanation:
10000*4 + 5000*4 + 2500*4 : 12,000*4 + 6000*4 + 3000*4
100 + 50 + 25 : 120 + 60 + 30
20 + 10 + 5 : 24 + 12 + 6
35 : 42
So (35/77) * x = 10,500
Solve, x = 23,100

A work which is completed by 24 men in 12 days is completed by 36 women in 14 days. 36 men started the work and worked for 6 days, after which they are replaced by some women. If the remaining work is to be completed in 3 days, what is the number of women required to be employed?

Explanation: 
24 m in 12 days, so 36 men in (24*12)/36 = 8 days
They did work for 6 days, so work completed by them is (6/8) = 3/4
Remaining work = 1 – 3/4 = 1/4
36 women do 1 work in 14 days
Let x women have to complete 1/4 of work in 3 days, so
36*14*(1/4) = x*3*(1)
Solve, x = 42 women

Monthly salaries of A and B is in the ratio 3 : 5 and that of C and B is 5 : 4 respectively. If there total monthly salary is Rs 1,33,000, then what is the combined monthly salary of B and C?

1.   Explanation:
A/B = 3/5 , B/C = 4/5
So A : B : C = 3*4 : 5*4 : 5*5 = 12 : 20 : 25
Combined salary of B and C = (20+25)/(12+20+25) * 1,33,000