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- Question
A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?
Options- A. 11 days
- B. 13 days
- C.
20 3 days 17 - D. None of these
- Correct Answer
- 13 days
ExplanationRatio of times taken by A and B = 100 : 130 = 10 : 13.Suppose B takes x days to do the work.
Then, 10 : 13 :: 23 : x ⟹ x = ❨ 23 x 13 ❩ ⟹ x = 299 . 10 10 A's 1 day's work = 1 ; 23 B's 1 day's work = 10 . 299 (A + B)'s 1 day's work = ❨ 1 + 10 ❩ = 23 = 1 . 23 299 299 13 Therefore, A and B together can complete the work in 13 days.
Time and Work problems
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- 1. A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
Options- A. 23 days
- B. 37 days
- C. 37½
- D. 40 days Discuss
Correct Answer: 37½
Explanation:
Whole work is done by A in ❨ 20 x 5 ❩ = 25 days. 4 Now, ❨ 1 - 4 ❩ i.e., 1 work is done by A and B in 3 days. 5 5 Whole work will be done by A and B in (3 x 5) = 15 days.
A's 1 day's work = 1 , (A + B)'s 1 day's work = 1 . 25 15 ∴ B's 1 day's work = ❨ 1 - 1 ❩ = 4 = 2 . 15 25 150 75 So, B alone would do the work in 75 = 37 1 days. 2 2 - 2. A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
Options- A. 8 hours
- B. 10 hours
- C. 12 hours
- D. 24 hours Discuss
Correct Answer: 12 hours
Explanation:
A's 1 hour's work = 1 ; 4 (B + C)'s 1 hour's work = 1 ; 3 (A + C)'s 1 hour's work = 1 . 2 (A + B + C)'s 1 hour's work = ❨ 1 + 1 ❩ = 7 . 4 3 12 B's 1 hour's work = ❨ 7 - 1 ❩ = 1 . 12 2 12 ∴ B alone will take 12 hours to do the work.
- 3. A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:
Options- A. 5 days
- B. 6 days
- C. 10 days
- D.
10 1 days 2
Discuss
Correct Answer: 10 days
Explanation:
(B + C)'s 1 day's work = ❨ 1 + 1 ❩ = 7 . 9 12 36 Work done by B and C in 3 days = ❨ 7 x 3 ❩ = 7 . 36 12 Remaining work = ❨ 1 - 7 ❩ = 5 . 12 12 Now, 1 work is done by A in 1 day. 24 So, 5 work is done by A in ❨ 24 x 5 ❩ = 10 days. 12 12 - 4. A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:
Options- A.
1 day 24 - B.
7 day 24 - C.
3 3 days 7 - D. 4 days Discuss
Correct Answer:3 3 days 7
Explanation:
Formula: If A can do a piece of work in n days, then A's 1 day's work = 1 . n (A + B + C)'s 1 day's work = ❨ 1 + 1 + 1 ❩ = 7 . 24 6 12 24 Formula: If A's 1 day's work = 1 , then A can finish the work in n days. n So, all the three together will complete the job in ❨ 24 ❩ days = 3 3 days. 7 7 - 5. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
Options- A. 30 days
- B. 40 days
- C. 60 days
- D. 70 days Discuss
Correct Answer: 60 days
Explanation:
Let A's 1 day's work = x and B's 1 day's work = y.Then, x + y = 1 and 16x + 44y = 1. 30 Solving these two equations, we get: x = 1 and y = 1 60 60 ∴ B's 1 day's work = 1 . 60 Hence, B alone shall finish the whole work in 60 days.
- 6. 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?
Options- A. 40
- B. 50
- C. 54
- D. 60 Discuss
Correct Answer: 60
Explanation:
(A + B)'s 20 day's work = ❨ 1 x 20 ❩ = 2 . 30 3 Remaining work = ❨ 1 - 2 ❩ = 1 . 3 3 Now, 1 work is done by A in 20 days. 3 Therefore, the whole work will be done by A in (20 x 3) = 60 days.
- 7. The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned half-yearly is:
Options- A. Rs. 2.50
- B. Rs. 3
- C. Rs. 3.75
- D. Rs. 4
- E. None of these Discuss
Correct Answer: Rs. 3
Explanation:
S.I. = Rs ❨ 1200 x 10 x 1 ❩ = Rs. 120. 100 C.I. = Rs. [ 1200 x ❨ 1 + 5 ❩ 2 - 1200 ] = Rs. 123. 100 ∴ Difference = Rs. (123 - 120) = Rs. 3.
- 8. If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time?
Options- A. Rs. 51.25
- B. Rs. 52
- C. Rs. 54.25
- D. Rs. 60 Discuss
Correct Answer: Rs. 51.25
Explanation:
Sum = Rs. ❨ 50 x 100 ❩ = Rs. 500. 2 x 5 Amount = Rs. [ 500 x ❨ 1 + 5 ❩ 2 ] 100 = Rs. ❨ 500 x 21 x 21 ❩ 20 20 = Rs. 551.25 ∴ C.I. = Rs. (551.25 - 500) = Rs. 51.25
- 9. Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit?
Options- A. Rs. 8600
- B. Rs. 8620
- C. Rs. 8820
- D. None of these Discuss
Correct Answer: Rs. 8820
Explanation:
Amount = Rs. [ 8000 x ❨ 1 + 5 ❩ 2 ] 100 = Rs. ❨ 8000 x 21 x 21 ❩ 20 20 = Rs. 8820. - 10. The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:
Options- A. 6.06%
- B. 6.07%
- C. 6.08%
- D. 6.09% Discuss
Correct Answer: 6.09%
Explanation:
Amount of Rs. 100 for 1 year
when compounded half-yearly] = Rs. [ 100 x ❨ 1 + 3 ❩ 2 ] = Rs. 106.09 100 ∴ Effective rate = (106.09 - 100)% = 6.09%
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