BANK & INSURANCE (TIME AND WORK & PIPE AND CISTERN) PART 1

Total Questions: 60

31. The number of days in which A and B together can finish a piece of work is 12 days less than the time taken by A alone and 27 days less than the time taken by B alone to finish the same work. If A and B completed the work in 15 days with the help of C and got a total compensation of Rs 3000 for the work, then what is the share of C?

Correct Answer: (d) Rs 500  
Solution:Let the number of days in which the work is completed by A and B together be n.
Then A takes (n + 12) days and B takes (n + 27) days to finish the work alone.
1/(n+12) + 1/(n+27) = 1/n
=> n[(n + 12) + (n + 27)] = (n + 12)(n + 27)
=> 2n² + 39n = n² + 39n + 324
=> n² = 324 ⇒ n = 18
So, if the total work is 1 unit then the work done by both A and B together in one day is 1/18 unit.
Total work done by these two in 15 days = 15/18 = 5/6th of work
So the work done by C = 1/6th of the total work
The money which C will get = 3000/6 = Rs. 500

32. The wages of a man for a day’s work is Rs 4 and for a woman it is Rs 2.The ratio of efficiency of a man to that of a woman is 3 : 2. A certain work is there which can be completed by employing 50 men for 80 days. How much cost saving will be there if we employ 20 men and 30 women instead of 50 men?

Correct Answer: (c) Rs 2000
Solution:The ratio of efficiency of a man to a woman is 3 : 2.
Suppose the work done by a man in 1 day is 3a units and by a woman is 2a units.
So the total work done by 50 men in one day = 50 × 3a = 150a units
It takes 80 days to finish the work, so total work = 150a × 80 unit = 12000a units
Since wage of a man per day is Rs 4 so cost of 1 day's work = 50 × 4 = Rs 200
It takes 80 days to finish the work so total cost of the work = 200 × 80 = Rs 16000
Now total work done by 20 men and 30 women in one day = 20 × 3a + 30 × 2a = 120a unit
As we know that total work done
= Amount of work done in one day × number of days worked
Hence, the number of days taken by 20 men and 30 women to finish the work = (12000a/120a) = 100 days
Cost of one day's work when 20 men and 30 women work = 20 × 4 + 30 × 2 = Rs 140
So total cost of the work in this case = Rs 140 × 100 = Rs 14000
Savings = Rs (16000 - 14000) = Rs 2000

33. Ram and Shyam can complete a work alone in 60 and 40 days respectively. They started doing the work together and after four days Shyam was replaced by Ajay and 8 days after that Shyam replaced Ram. Find the total number of days in which work gets complete if Ajay can complete the work alone in double the no. of days in which Ram and Shyam together complete the work.

Correct Answer: (e) 23 7/11 days
Solution:Work completed by Ram alone = 60 days
Work completed by Shyam alone = 40 days
Work completed by Ajay alone = 2/(1/60 + 1/40)
= 2 × 24 = 48 days
Now,
For 4 days work done by Ram and shyam
= 4 × (1/60 + 1/40) = 4/24 = 1/6
For 8 days work done by Ram and Ajay = 8 × (1/60 + 1/48) = 3/10
Remaining work = 1 - (1/6 + 3/10) = 8/15
This is completed by Shyam and Ajay in 'N' days (let)
So,
N × (1/40 + 1/48) = 8/15
N × (11/240) = 8/15
N = 128/11 days = 11(7/11) days
Total no. of days in which work gets completed = 4 + 8 + 128/11 = 23(7/11) days

34. Ash can do a job in 10 days. Bali can do the same job in 5 days. In how many days they can complete the job if they work together?

Correct Answer: (b) 3.33 days  
Solution:Ash can do a job in 10 days, So efficiency of Ash = 100/10 = 10%
Similarly, Bali's efficiency = 100/5 = 20%
Combined efficiency of Ash + Bali per day becomes = 20 + 10 = 30%
Now, we have to find out the number of days taken by both Ash and Bali to do 100% work,
Since they can do 30% work in 1 day,
So, they will 100% work in 100/30 = 3.33 days

35. A can write 75 pages in 25 hrs. A and B together can write 135 pages in 27 hrs. In what time can B write 42 pages?

Correct Answer: (d) 21  
Solution:

A can write 75/25 = 3 pages in 1 hr
A + B can 135/27 = 5 pages in 1 hr
B can write 5 - 3 = 2 pages in 1 hr
Time taken of B = 42/2 = 21 hrs

36. Ram and Ritesh can do a piece of work in 24 and 30 days respectively. They both started and worked for 6 days. Ritesh then leaves the work and another their friend Ronie joins the work and completed the remaining work with Ram in 11 days. Find how many days are taken by Ronie alone to finish the work?

Correct Answer: (d) 120 days  
Solution:(1/24 + 1/30) × 6 + (1/24 + 1/Ronie) × 11 = 1
Therefore, Ronie takes 120 days to finish the work.

37. A project can be completed by 2 men and 5 women in 8 days while 4 men and 6 women can complete the same in 5 days. How many men are required to complete the project in 4 days?

Correct Answer: (a) 8  
Solution:Let 'a' and 'b' be the amount of work done by each man and each woman respectively in a day.
8 × (2a + 5b) = 5 × (4a + 6b)
=> 4a = 10b
=> a = 2.5b
8 × (2a + 5b) = 1
=> 8 (2 × 2.5b + 5b) = 1
=> 80b = 1
=> b = 1/80
=> a = 1/32
So a man can complete the work in 32 days.
Therefore, 8 men are required to complete the work in 4 days

38. 10 men and 15 women can finish a work in 6 days. One man alone finished that work in 100 days. In how many days a woman alone can finish the work?

Correct Answer: (b) 225  
Solution:

Let the total work be 1 unit.
One man can finish this 1 unit work in 100 days means in one day 1 man can do 1/100 unit of work.

So 10 men can do = 10 × 1/100 = 1/10 unit of work.
According to the question 10 men and 15 women finish a work in 6 days means in 1 day they can finish 1/6th unit of work.
Hence, 15 woman's work of a day = 1/6 - 1/10 = 1/15 unit
∴ a woman alone will take
= 15 × 15 = 225 days

39. Pipe A can fill a cistern in 6 hours and pipe B can fill it in 8 hours. Both the pipes are opened simultaneously, but after two hours, pipe A is closed. How many hours will B take to fill the remaining part of the cistern?

Correct Answer: (b) 3 1/3  
Solution:Let the time taken by pipe B to fill the remaining part be x hours.
(2/6) + (x+2)/8 = 1
(4×2 + 3(x+2))/24 = 1
3(x+2) = 16
x = 16/3 - 2 = 10/3 = 3⅓

40. Pia and Ria can complete a project together in 26 days. Pia alone can complete the project in 78 days. They start working together but Pia leaves the job after 12 days. In how many days can Ria complete the remaining work of the project?

Correct Answer: (d) 21 days  
Solution:Let the total work be 78 units (LCM of 26, 78).
So, work done by Pia and Ria together = 78/26 = 3 units/day
Work done by Pia = 78/78 = 1 units/day
So, work done by Ria = 3 - 1 = 2 units/day
Work done for 12 days = 12 × 3 = 36 units
Remaining work = 78 - 36 = 42 units
Hence, no. of days taken by Ria = 42/2 = 21 days