BANK & INSURANCE (TIME AND WORK & PIPE AND CISTERN) PART 2

Total Questions: 60

11. Rahul is twice as good at building a wall as Shiv. together they can build the wall in 12 days, in how many days can Rahul alone build the wall?

Correct Answer: (c) 18 days
Solution:the efficiency of Rahul : Shiv = 2 : 1
time taken by Rahul : Shiv = 1 : 2
let time taken by Rahul be x and by Shiv be 2x
their one day work together will be = 1/x + 1/2x = 3/2x
their actual one day work is 1/12
So, 3/2x = 1/12 ⇒ x = 18 days

12. A can do one-third of a work in 12 days and B can do half the same work in 9 days. Working together, in how many days they can do nine-fourth of the work?

Correct Answer: (d) 27 days 
Solution:A can do the whole work in = 12 × 3 = 36 days
B can do the whole work in = 9 × 2 = 18 days
(A+B)’s one day work = 1/18 + 1/36 = 1/12
Time taken to complete the whole work = 12 days
Time taken to complete nine-fourth of the work = 9/4 × 12 = 27 days

13. P alone can finish the work in 15 hours and Q alone can finish the work in 20 hours while R alone can finish the work in N hours. All three worked for 5 hours, after that P left the work and remaining work gets completed in 3 hours. Find the value of N.

Correct Answer: (b) 30  
Solution:

(P + Q + R)’s 1 hours work = 1/15 + 1/20 + 1/N
= 7/60 + 1/N
(P + Q + R)’s 5 hours work = 5 × (7/60 + 1/N)
= 7/12 + 5/N
Remaining work = 1 - (7/12 + 5/N) = 5/12 - 5/N
(Q + R)’s 1 hour’s work = 1/20 + 1/N
Then,
⇒ [1/(1/20 + 1/N)] × (5/12 - 5/N) = 3

⇒ (5N - 60)/12N = 3 × (20 + N)/20N
⇒ 25N - 300 = 180 + 9N
∴ N = 30

14. 30 boys can complete the work in 10 days while 25 girls can complete the work in 20 days. In how many days 10 boys and 10 girls can complete the work?

Correct Answer: (d) 75/4 days  
Solution:

1 boy's 1 day's work = 1/(30 × 10)
1 girl's 1 day's work = 1/(25 × 20)

Then, 10 boys 1 days work = 10/(30 × 10) = 1/30
10 Girls 1 days work = 10/(25 × 20) = 1/50
⇒ (10 boys + 10 girls)’s 1 days work = 1/30 + 1/50 = 8/150 = 4/75

In 75/4 days 10 boys and 10 girls can complete the work.

15. A alone can complete the work in 30 days while B alone can complete the work in 25 days. With the help of C they can complete the work in 50/7 days. If they took this work for 4200, find the difference between the shares of C and A.

Correct Answer: (d) Rs.1000  
Solution:

A’s 1 day’s work = 1/30
B’s 1 day’s work = 1/25
⇒ (A + B + C)’s 1 day’s work = 7/50
⇒ 1/C = 7/50 - 1/30 - 1/25 = 1/15
C’s 1 days work = 1/15

Ratio of their work done =
= 1/30 : 1/25 : 1/15
= 5 : 6 : 10

The profit share of A = 5/21 × 4200 = Rs.1000
The profit share of C = 10/21 × 4200 = Rs.2000
∴ Required difference = 2000 - 1000 = Rs.1000

16. 5 men and 6 women can finish a work in 12 days whereas 8 men and 4 women can finish the same work in 8 days. How long will 15 men and 18 women can complete the whole work?

Correct Answer: (a) 4  
Solution:

Let efficiency of a man be m
Let efficiency of a woman be w
Let x be the number of days 15 men and 18 women take to complete the work

[(5 × m) + (6 × w)] × 12 = [(8 × m) + (4 × w)] × 8
⇒ [(5 × m) + (6 × w)] × 3 = [(8 × m) + (4 × w)] × 2
⇒ [15m + 18w] = [16m + 8w]
⇒ [18w - 8w] = [16m - 15m]
⇒ [10w] = [1m]
⇒ m : w = 10 : 1

Total work = [(5 × m) + (6 × w)] × 12
⇒ [(5 × 10) + (6 × 1)] × 12
⇒ [56] × 12
⇒ Total work = 672

We know that,
(15m) + (18w) = (15 × 10) + (18 × 1)
⇒ 168

15 men and 18 women × x = Total work
⇒ 168 × x = 672
⇒ x = 672/168 = 4 days

∴ 15 men and 18 women can do the whole work in 4 days.

17. Aman and Chaman have been given the task of decorating a house for Rs.2400. With the help of Razia, they complete the job in just 6 days. Had Aman alone be doing the task, he would need 12 days. If Chaman alone would be doing the task, he would need 16 days. How much money will Razia get?

Correct Answer: (e) None of these
Solution:

Let total work = LCM of (6, 12, 16) = 48 units
Efficiency of Aman = 48/12 = 4 units per day
Efficiency of Chaman = 48/16 = 3 units per day
Efficiency of (Aman + Chaman + Razia) = 48/6 = 8 units per day
Efficiency of Razia = 8 - 4 - 3 = 1

Share of Razia = 1/8 × 2400 = Rs 300

18. A can do a work in 12 days and B can do the same work in 24 days.They will be given Rs 240 for the work.They work along with a third man and take 4 days to complete it.Find out the share of the third man?

Correct Answer: (c) Rs 120
Solution:

Let the total work be X
A can do the work in 12 days, So, 1 day work of A = X/12
B can do the work in 24 days, So, 1 day work of B = X/24
Let the Third man complete the work in “Y” days

So, 1 day work of Third man = X/Y

They all start working together and complete the work in 4 days. according to the question:
4 (X/12 + X/24 + X/Y) = X
1/3 + 1/6 + 4/Y = 1
2Y + Y + 24
—————— = 1
6Y
3Y + 24 = 6Y
Y = 8

1 day work of Third man = X/8

Amount of work done by Third man = 4X/8 = X/2

Share of Third man out of 240 = X/2 × 240/X = Rs 120

19. 10 women can complete a work in 9 days and 10 children takes 18 days to complete the work. How many days will 5 women and 10 children take to complete the work?

Correct Answer: (a) 9 days  
Solution:

10 women’s 1 day’s work = 1/9
1 women’s 1 day’s work = 1/90

10 children’s 1 day’s work = 1/18
1 children’s 1 day’s work = 1/180

(5 women + 10 children)’s 1 day’s work = (5 × 1/90 + 10 × 1/180)
= 1/18 + 1/18 = 1/9

5 women and 10 children will finish the work in 9 days

20. Raunak and Baua are working on a project. Raunak take 12 hours to type 64 pages of the project, while Baua takes 10 hours to type 80 pages. If they started at same time, then how much time will they take, working together on two different computers to type a project of 220 pages?

Correct Answer: (c) 16 hours and 30 minutes
Solution:

Number of pages Raunak can type in one hour
= 64/12 = 16/3 pages

80 Number of pages Baua can type in one hour.
= 80/10 = 8 pages

(Raunak : Baua)’s one hour’s work = 32/6 : 8
= 32 : 48 = 2 : 3

Total pages = 220

Number of pages typed by Raunak = 220 × 2/5 = 88 pages
Number of pages typed by Baua = 220 - 88 = 132 pages

Time taken by Raunak to type 88 pages = 88 × 3/16 = 16 hours and 30 minutes
Time taken by Baua to type 132 pages = 132/8 = 16 hours and 30 minutes