Time and Work Problems with Solutions for Bank Exams

Time and Work Problems with Solutions for Competitive Exams

Q.11. 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

(A) 40

(B) 35

(C) 50

(D) 45

$$ Then, \ 4x + 6y= {1\over8} \ and \ 3x+7y= {1\over10} $$

$$ Solving \ the \ two \ equations, \ we \ get: \ x = {11\over400}, y = {1\over400}$$

$$ ∴  1 \ woman's \ 1 \ day's \ work = {1\over400} $$

$$ → 10 \ women's \ 1 \ day's \ work = \left({1\over400}× 10 \right) = {1\over40} $$

Hence, 10 women will complete the work in 40 days.

Q.12. A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?

(A) 7

(B) 5

(C) 8

(D) 6

$$ Remaining \ work = \left(1-{2\over3} \right)={1\over3} $$

$$ \ Now, \ {1\over18} \ work\ is\ done \ by \ A \ in \ 1 \ day.$$

$$ ∴ \ {1\over3} \   work \ is \ done \ by \ A \ in \ \left(18×{1\over3} \right)= 6 days \ $$

Q.13. A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work?

(A) 50

(B) 40

(C) 60

(D) 54

$$ Remaining \ work = \left(1-{2\over3} \right)={1\over3} $$

Now, 1/3 work is done by A in 20 days.

Therefore, the whole work will be done by A in (20 x 3) = 60 days

Q.14.10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

(A) 5

(B) 7

(C) 3

(D) None of these

(E) Cannot be determined

$$ 1 \ child's \ 1 \ day's \ work = {1\over70}$$

(5 women + 10 children)'s day's work = $$ {5\over70}+{10\over140}= {1\over14}+{1\over14}= {1\over7} $$

5 women and 10 children will complete the work in 7 days.

Q.15. P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?

$$ (A) \ 5{6\over11}$$

$$ (B) \ 5{5\over11}$$

$$ (C) \ 6{6\over11}$$

$$ (D) \ 6{5\over11}$$

Q can complete the work in (8 x 10) hrs. = 80 hrs.

$$ ⸫ \ P's \ 1 \ hour's \ work \ = {1\over96} $$

$$ and \ Q's \ 1 \ hour's \ work \ = {1\over80} $$

(P + Q)'s 1 hour's work =  

$$\left({1\over96}+{1\over80}={11\over480} \right)$$

So, both P and Q will finish the work in (480/11) hrs.

⸫  Number of days of 8 hours each = $$ \left({480\over11}×{1\over8} \right)={60\over11} \ days = 5{5\over11} days $$

I hope these solutions was helpful for your competitive exams. If you are not able to understand properly you can ask me in the comment section related time and work problems with solutions. Visit next page for more Time and Work problems.