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- Question
A and B can do a job together in 7 days. A is 1¾ times as efficient as B. The same job can be done by A alone in :
Options- A.
9 1 days 3 - B. 11 days
- C.
12 1 days 4 - D.
16 1 days 3 - Correct Answer
- 11 days
Explanation(A's 1 day's work) : (B's 1 day's work) = 7 : 1 = 7 : 4. 4 Let A's and B's 1 day's work be 7x and 4x respectively.
Then, 7x + 4x = 1 ⟹ 11x = 1 ⟹ x = 1 . 7 7 77 ∴ A's 1 day's work = ❨ 1 x 7 ❩ = 1 . 77 11
Time and Work problems
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- 1. X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?
Options- A.
13 1 days 3 - B. 15 days
- C. 20 days
- D. 26 days Discuss
Correct Answer:13 1 days 3
Explanation:
Work done by X in 8 days = ❨ 1 x 8 ❩ = 1 . 40 5 Remaining work = ❨ 1 - 1 ❩ = 4 . 5 5 Now, 4 work is done by Y in 16 days. 5 Whole work will be done by Y in ❨ 16 x 5 ❩ = 20 days. 4 ∴ X's 1 day's work = 1 , Y's 1 day's work = 1 . 40 20 (X + Y)'s 1 day's work = ❨ 1 + 1 ❩ = 3 . 40 20 40 Hence, X and Y will together complete the work in ❨ 40 ❩ = 13 1 days. 3 3 - 2. Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?
Options- A. 8 kmph
- B. 11 kmph
- C. 12 kmph
- D. 14 kmph Discuss
Correct Answer: 12 kmph
Explanation:
Let the distance travelled by x km.Then, x - x = 2 10 15 ⟹ 3x - 2x = 60
⟹ x = 60 km.
Time taken to travel 60 km at 10 km/hr = ❨ 60 ❩hrs = 6 hrs. 10 So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
∴ Required speed = ❨ 60 ❩kmph. = 12 kmph. 5 - 3. A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is:
Options- A. 35
- B.
36 2 3 - C.
37 1 2 - D. 40 Discuss
Correct Answer: 40
Explanation:
Let distance = x km and usual rate = y kmph.Then, x - x = 40 ⟹ 2y(y + 3) = 9x ....(i) y y + 3 60 And, x - x = 40 ⟹ y(y - 2) = 3x ....(ii) y -2 y 60 On dividing (i) by (ii), we get: x = 40.
- 4. It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:
Options- A. 2 : 3
- B. 3 : 2
- C. 3 : 4
- D. 4 : 3 Discuss
Correct Answer: 3 : 4
Explanation:
Let the speed of the train be x km/hr and that of the car be y km/hr.Then, 120 + 480 = 8 ⟹ 1 + 4 = 1 ....(i) x y x y 15 And, 200 + 400 = 25 ⟹ 1 + 2 = 1 ....(ii) x y 3 x y 24 Solving (i) and (ii), we get: x = 60 and y = 80.
∴ Ratio of speeds = 60 : 80 = 3 : 4.
- 5. In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:
Options- A. 5 kmph
- B. 6 kmph
- C. 6.25 kmph
- D. 7.5 kmph Discuss
Correct Answer: 5 kmph
Explanation:
Let Abhay's speed be x km/hr.Then, 30 - 30 = 3 x 2x ⟹ 6x = 30
⟹ x = 5 km/hr.
- 6. A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
Options- A.
9 1 days 5 - B.
9 2 days 5 - C.
9 3 days 5 - D. 10 Discuss
Correct Answer:9 3 days 5
Explanation:
(A + B + C)'s 1 day's work = 1 , 4 A's 1 day's work = 1 , 16 B's 1 day's work = 1 . 12 ∴ C's 1 day's work = 1 - ❨ 1 + 1 ❩ = ❨ 1 - 7 ❩ = 5 . 4 16 12 4 48 48 So, C alone can do the work in 48 = 9 3 days. 5 5 - 7. A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :
Options- A. 8 days
- B. 10 days
- C. 12 days
- D. 15 days Discuss
Correct Answer: 12 days
Explanation:
(A + B)'s 1 day's work = ❨ 1 + 1 ❩ = 1 . 15 10 6 Work done by A and B in 2 days = ❨ 1 x 2 ❩ = 1 . 6 3 Remaining work = ❨ 1 - 1 ❩ = 2 . 3 3 Now, 1 work is done by A in 1 day. 15 ∴ 2 work will be done by a in ❨ 15 x 2 ❩ = 10 days. 3 3 Hence, the total time taken = (10 + 2) = 12 days.
- 8. A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
Options- A. 12 days
- B. 15 days
- C. 16 days
- D. 18 days Discuss
Correct Answer: 15 days
Explanation:
A's 2 day's work = ❨ 1 x 2 ❩ = 1 . 20 10 (A + B + C)'s 1 day's work = ❨ 1 + 1 + 1 ❩ = 6 = 1 . 20 30 60 60 10 Work done in 3 days = ❨ 1 + 1 ❩ = 1 . 10 10 5 Now, 1 work is done in 3 days. 5 ∴ Whole work will be done in (3 x 5) = 15 days.
- 9. A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?
Options- A. 18 days
- B. 24 days
- C. 30 days
- D. 36 days Discuss
Correct Answer: 18 days
Explanation:
2(A + B + C)'s 1 day's work = ❨ 1 + 1 + 1 ❩ = 15 = 1 . 30 24 20 120 8 Therefore, (A + B + C)'s 1 day's work = 1 = 1 . 2 x 8 16 Work done by A, B, C in 10 days = 10 = 5 . 16 8 Remaining work = ❨ 1 - 5 ❩ = 3 . 8 8 A's 1 day's work = ❨ 1 - 1 ❩ = 1 . 16 24 48 Now, 1 work is done by A in 1 day. 48 So, 3 work will be done by A in ❨ 48 x 3 ❩ = 18 days. 8 8 - 10. 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?
Options- A. 35
- B. 40
- C. 45
- D. 50 Discuss
Correct Answer: 40
Explanation:
Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.Then, 4x + 6y = 1 and 3x + 7y = 1 . 8 10 Solving the two equations, we get: x = 11 , y = 1 400 400 ∴ 1 woman's 1 day's work = 1 . 400 ⟹ 10 women's 1 day's work = ❨ 1 x 10 ❩ = 1 . 400 40 Hence, 10 women will complete the work in 40 days.
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