Check Your QUANT Concepts - 2

TIME & WORK

1. C takes twice the number of days to do a piece of work than A takes. A and B together can do it in 6 days while B and C together can do it in 10 days. In how many days A can alone do the work ?

a. 60

b. 30

c. 6

d. 7.5

2. 30 workers can finish a work in 20 days. After how many days should 9 workers leave the job so that the work is completed in total 26 days ?

a. 12

b. 10

c. 6

d. None of these

3. Harry can do a work in 40 days when working alone. He alone worked at it for 8 days and then Raman completed the remaining work in 24 days. In how many days they will finish the whole work, working together ?

a. 17 1/7

b. 18 1/7 

c. 9 1/6 

d. 14 

4. A group of men decided to do a job in 4 days. But since 20 men dropped out every day, the job completed at the end of the 7th day. How many men were there at the beginning ?

a. 240

b. 140

c. 280

d. 150

5. The total number of men, women and children working in a factory is 18. They earn Rs. 4000 in a day. If the sum of the wages of all men, all women and all children is in the ratio of 18:10:12  and if the wages of an individual man, woman and child is in the ratio 6:5:3, then how much a woman earn in a day ?

a. Rs. 400

b. Rs. 250

c. Rs. 150

d. Rs. 120

# Answers
1. A+B -->> 6 days
B+C -->> 10 days
Let their LCM 60 be the total work.
Now, its given in question A's efficiency is twice the efficiency of B.
A+B's efficiency -->> 60/6 -->> 10
And, B+C's efficiency -->> 60/10 -->> 6
Replace A by 2C
So, 2C + B = 10, and
B+C = 6
Solving above two equations, we will get
C= 4
B= 2
A= 8
So work done by A in, 60/8 -->> 7.5 days

2. 30*20 = 30*x + 21*(26-x)
By solving this, you will get x=6
i.e. , after 6 days.

3. Let total work be 40
Then Harry's efficiency will be 40/40 -->> 1
Harry worked for 8 days, means 8 work has been already done when Harry left the job.
Remaining work -->> 40-8 -->> 32
Now, Raman completed the remaining work in 24 days, his efficiency will be, 32/24 -->> 4/3
Now, working together, their combined efficiency will be -->> 1+4/3 -->> 7/3
Work will be completed in -->> 40/(7/3) -->> 120/7 -->> 17 1/7

4. Method -1
Go through options:
140*4 = (140 + 120 + 100 + ----- + 20)
560 = 560
Method -2
Let n be the initial number of worker then,
n*4 = n + (n-20) + (n-40) + ----- + (n-120)
4n = 7n - 420
3n = 420
n = 140 workers

5. Ratio of men, women and children = 18/6 : 10/5 : 12/3 -->> 3x:2x:4x
Now, 2x + 3x + 4x = 18
x = 2
Therefore, number of women -->> 4
Share of all women -->> 10/(18+10+12) *4000 -->> 1000 Rs.

So, share of each women = 1000/4 = Rs. 250