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

Total Questions: 60

1. 12 men or 15 women can do a piece of work in 9 days. If 4 men work on every odd day and 3 women work on every even day. If on the last day men turn they didn’t come to work and women have to work at the place of men then find in how many days they will complete the work.

Correct Answer: (c) 103/3 day 
Solution:12 men or 15 women can complete the work in 9 days. 4 men and 3 women work alternate day and last day men didn’t come.
Concept:
We will try to solve the question by the LCM method.
Calculation:
12 men can complete the work in 9 days
⇒ 1 man can complete it in 108 days
15 women can complete the work in 9 days
⇒ 1 woman can complete it in 135 days
Let the total work be LCM of 108 and 135 = 540 unit
Efficiency of 1 man = 540/108 = 5 unit
And efficiency of 1 woman = 540/135 = 4 unit
According to question:
⇒ 2 days work = (4 men work + 3 women work)
⇒ (4×5 + 3×4) = 32 unit
⇒ 32-days work = 512 unit
Remaining work = 540 - 512 = 28 units which is less than 32 units
⇒ If 4 men work on 33rd day it will be their last day
so on 33rd day 3 women will work in place of men,
⇒ 33rd days work = 512 + 12 = 524
⇒ 34th days work = 524 + 12 = 536
Remaining work completed by women in 1/3 day
∴ The total work completed in (34 + 1/3) = 103/3 day

2. Three workers A, B and C can do a piece of work in 16, 20 and 24 hours respectively. They started the work together but after (P – 8) hours, A left the job. ‘P’ hours before completion of the work B has left. The whole work is completed in (P + 5) hours. What is the value of ‘P’?

Correct Answer: (a) 10 hours  
Solution:

Number of hours A worked = (P - 8)
Number of hours B worked = P + 5 = P - 5 hours
Number of hours C worked = (P + 5) hours
∴ (P + 8)/16 + 5/20 + (P + 5)/24 = 1

⇒ [15(P - 8) + 60 + 10(P + 5)]/240 = 1
⇒ 15P - 120 + 60 + 10P + 50 = 240
⇒ 25P = 250
⇒ P = 10 hours

3. Aditya and Shifa took a work to complete total amount of Rs. 360. Aditya can do a work in 20 days while Shifa can do the same work in 30 days. They started the work together and after some days they thought to take the help of Ajay and with the help of Ajay they completed the work in 7 days. Find the Share of Ajay.

Correct Answer: (c) Rs. 150
Solution:

Let the total work be x
As given, Aditya can do the work in 20 days
So, Efficiency of Aditya per day = x/20 work
Shifa can do the work in 30 days
So, Efficiency of Shifa per day = x/30 work
Total work done by Aditya and Shifa in one day = (x/20) + (x/30)
⇒ Total work done by Aditya and Shifa in one day = 5x/60 work
Now, Total work is completed in 7 days
So, Total work done by Aditya and Shifa in 7 days = 5x/60 × 7
⇒ Total work done by Aditya and Shifa in 7 days = 35x/60 work
Now, Work done by Ajay = (Total work - Work done by Aditya and Shifa in 7 days)
⇒ Work done by Ajay = x - (35x/60) work
⇒ Work done by Ajay = 25x/60 work
Now, the share of Ajay will be proportional to the amount of work done by him
So, Share of Ajay = (Work done by Ajay/Total work) × Total Amount
⇒ Share of Ajay = (25x/60)/x × 360
⇒ Share of Ajay = Rs.150
∴ The Share of Ajay is Rs.150

4. A is as efficient as B and C together. Working together A and B can complete a work in 36 days and C alone can complete it in 60 days. A and C work together for 10 days. B alone will complete the remaining work in:

Correct Answer: (b) 110 days  
Solution:Efficiency ratio of A to (B and C) = 1 : 1 ---- (1)
Time ratio of (A and B) to C = 36 : 60 = 3 : 5
As we know,
Efficiency is inversely proportional to time.
Efficiency ratio of (A and B) to C = 5 : 3 ---- (2)
Multiply by 4 in equation (1)
Efficiency ratio of A to (B and C) = 4 : 4 ---- (3)
Now we can say, from equation (2) and equation (3)
Efficiency of A = 4 and efficiency of C = 3 and
efficiency of B = 4 - 3 = 1
Total work = 3 × 60 = 180
Work done by A and C in done days = (4 + 3) × 10 = 7 × 10 = 70
Remaining work = 180 - 70 = 110
Remaining work done by B alone in = 110/1 = 110 days

5. A and B were hired to do work for Rs. 11000, out of which B received Rs. 4125 for his work. If they completed the work in 15/2 days, in how many days would A have done the work alone?

Correct Answer: (c) 12 days
Solution:Let A take ‘x’ days to do the work alone
A’s 1 day work = 1/x
A’s share = 11000 - 4125 = Rs. 6875
Now, ratio of their wages = ratio of their 1 day work
6875 : 4125 = 1/x : (B’s 1 day work)
⇒ B’s 1 day work = (4125/6875) × 1/x = 3/5x
They together completed the work in 15/2 days
⇒ A’s 1 day work + B’s 1 day work = 2/15
⇒ 1/x + 3/5x = 2/15
⇒ 8/5x = 2/15
⇒ x = (8/2) × (15/5) = 12
∴ A can do the work alone in 12 days

6. 2 men and 1 woman can finish a piece of work in 12 days while 4 women and 2 men can do the same work in 8 days. If a man gets Rs 75 per day and wages per day for a woman is Rs x, then what will be the value of (x² + 50)?

Correct Answer: (d) 950  
Solution:

(2 men + 1 woman)’s 1 day work = 1/12
⇒ (2 × 12 men + 1 × 12 women) can finish the work in 1 day
Also, (4 woman + 2 men)’s 1 day work = 1/8
⇒ (4 × 8 women + 2 × 8 men) can finish the whole work in 1 day
∴ (24 men + 12 women) = (32 women + 16 men)
⇒ 8 men = 20 women

Now, 8 men will get = 8 × 75 = Rs 600 per day.
⇒ 20 women will get = Rs 600 per day.
∴ 1 woman will get = Rs 600/20
⇒ Rs 30 per day.
⇒ The value of x = 30
⇒ (x² + 50) = 30² + 50
⇒ 900 + 50
⇒ 950
∴ The value of (x² + 50) is 950

7. A and B completed work together in 6 days. Had A worked 1/3rd of his efficiency and B's efficiency remained the same, then it would have taken them 10 days to complete the task. How much time would it take for A alone to complete the work?

Correct Answer: (e) None of these
Solution:

Let efficiency of A and B be A and B respectively
According to question,
(A + B) × 6 = [(A/3) + B] × 10
(A + B) × 3 = [(A/3) + B] × 5
⇒ 3A + 3B = (5A/3) + 5B
⇒ 3A - (5A/3) = 5B - 3B
⇒ 4A/3 = 2B
⇒ 4A = 6B
⇒ 2A = 3B
⇒ A = 3 and B = 2
Total work = (A + B) × 6 = (3 + 2) × 6 = 5 × 6 = 30
Time taken by A alone to complete the work = 30/3 days
⇒ 10 days

8. P can complete a work in 30 days when working alone. P works for 6 days and then leaves. The remaining work is completed by Q and R in 12 days. If R alone can finish half of the work in 8 days, then find the number of days that Q will take to finish the whole work, working alone.

Correct Answer: (c) 240 days
Solution:

P’s 1 day work = 1/30
⇒ 6 day work of P = 1/30 × 6 = 1/5
Remaining work = 1 - 1/5 = 4/5
This 4/5 work is completed by Q and R in 12 days.
∴ Time taken by Q and R together to finish the whole work = 12 × 5/4
⇒ 15 days

Now, R finishes 1/2 work in 8 days.
∴ R will finish the whole work alone in 8 × 2 days
⇒ 16 days.

∴ 1 day work of Q = 1/15 - 1/16 = 1/240 units
∴ Time taken by Q to finish the whole work, working alone is 240 days

9. Arun can do a piece of work in 10 days Ramesh in 15 days. They work together for 5 days. The rest of the work was finished by Naresh in 2 days. If they get Rs. 1,500 for the whole work, the daily wages of Ramesh and Naresh are___

Correct Answer: (c) 225
Solution:

Let assume total work = 30 units
⇒ Arun’s one day work = 3 units
⇒ Ramesh’s one day work = 2 units
If they work together for 5 days
⇒ Total work in 5 days = 5 × 3 + 5 × 2 = 25 units
The remaining work = 30 - 25 = 5 units
⇒ 5 units are completed by Naresh in 2 days.
So, Naresh one day work = 5/2 = 2.5 units

1 unit wage = 1500/30 = Rs. 50
If they get Rs. 1500 for 30 units work.
⇒ Ramesh’s and Naresh’s one day work = 2 + 2.5 = 4.5 units
So, Daily wage of Ramesh and Naresh = 50 × 4.5
⇒ Rs. 225

10. Efficiency of B is 20% less than that of A, While the efficiency of C is 25% less than that of B. If altogether they can complete the whole work in 5 days, then in how many days A can complete the whole work?

Correct Answer: (a) 12  
Solution:Let the efficiency of A be 5
Efficiency of B = 5 × 4/5 = 4
Efficiency of C = 4 × 3/4 = 3
Total work = (5 + 4 + 3) × 5 = 12 × 5 = 60
A alone can complete the whole work in
= 60/5 = 12 days