1. Ram and Shyam can complete a work together in 20 days. If Ram alone complete the work in 36 days, find the number of days Shyam alone will take to complete the task.
SHOW ANSWER
Correct Ans:45
Explanation:
Let the time taken by Ram alone to complete the work = R days = 36 days
the time taken by Shyam alone to complete the work = S days
Given, the time taken by Ram and Shyam = R + S days = 20 days
=> 1/(R + S) = (1/R) + (1/S)
=> 1 / 20 = (1 / 36) + (1 / S)
=> 1 / S = (1 / 20) - (1 / 36)
=> 1 / S = (36 - 20) / (20 * 36)
=> 1 / S = 16 / 720
Taking reciprocal on both sides
=> S = 720 / 16
=> S = 45 days.
Thus, the time taken by Shyam alone to complete the work = 45 days.
2. Ajay is twice efficient as Vijay. If Vijay can complete the work in 48 days, find the number days to complete the work if both work together.
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Correct Ans:16
Explanation:
3. Vicky and Arun can complete a piece of work in 15 and 10 days. What percentage of the work would have got completed in 3 days.
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Correct Ans:50 %
Explanation:
4. Vinay and Vicky can complete a piece of work in 30 and 15 days repectively by working alone. After how many days 80% of the work would have got completed?
SHOW ANSWER
Correct Ans:8 days
Explanation:
Let the time taken by Vinay = A days = 30 days
the time taken by Vicky = B days = 15 days
Vinay + Vicky together can complete 100 % of the work in:
=> 1/(A + B) = (1/A) + (1/B)
=> 1 / (A + B) = (1 / 30) + (1 / 15)
=> 1 / (A + B) = (15 + 30) / (30 * 15)
=> 1 / (A + B) = 45 / 450
Taking reciprocal on both sides
A + B = 450/45
A + B = 10 days
Thus 100% of the work is completed in 10 days,
80% of the work is completed in {(10 / 100%) * 80%} days = 8 days
5. If A and B can complete the work in 24 and 40 days, Find the number of days required by them to complete the work if they work together.
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Correct Ans:15 days
Explanation:
A can complete the work in 24 days.
B can complete the same work in 40 days.
A's 1 day work = 1/24
B's 1 day work = 1/40
(A + B)'s 1 day work = (1/24 + 1/40)
= (40 + 24) / 960
= 64 / 960
= 1 / 15
A and B can complete the work in 15days.
6. Ajay is twice efficient as Vijay. If both work together and complete a work in 10 days, find the number of days Ajay will take to complete the work.
SHOW ANSWER
Correct Ans:15
Explanation:
Let the time taken by Ajay = A days
the time taken by Vijay = V days
Given, Ajay is twice efficient as Vijay
=> If Ajay completes a work in x days, then Vijay can complete the same work in 2x days.
=> V = 2A
Given, A + V = 10 days
=> 1/(A + V) = (1/A) + (1/V)
=> 1/ 10 = (1/A) + (1/2A)
=> 1/ 10 = 3 / 2A
Taking reciprocal on both sides
=> 10 = 2A/3
=> 2A = 30
=> A = 15 days
Thus, Ajay completes a work in 15 days
7. Ram and Shyam can complete a work together in 9 days. If Ram alone can complete the work in 12 days, find the number of days taken by Shyam alone to complete the work.
SHOW ANSWER
Correct Ans:36 days
Explanation:
Let the time taken by Ram alone to complete the work = R days = 12 days
the time taken by Shyam alone to complete the work = S days
Given, the time taken by Ram and Shyam = R + S days = 9 days
=>1/(R + S) = (1/R) + (1/S)
=> 1 / 9 = (1 / 12) + (1 / S)
=> 1 / S = (1 / 9) - (1 / 12)
=> 1 / S = (12 - 9) / (9* 12)
=> 1 / S = 3 / 108
Taking reciprocal on both sides
=> S = 108 / 3
=> S = 36 days.
Thus,the time taken by Shyam alone to complete the work = 36 days.
8. A and B can complete a piece of work in 10 and 15 days. In how many days 50 % of the work will be completed?
SHOW ANSWER
Correct Ans:3
Explanation:
Let the time taken by A = 10 days
the time taken by B = 15 days
A + B together can complete 100 % of the work in:
=> 1/(A + B) = (1/A) + (1/B)
=> 1 / (A + B) = (1 / 10) + (1 / 15)
=> 1 / (A + B) = (15 + 10) / (10 * 15)
=> 1 / (A + B) = 25 / 150
Taking reciprocal on both sides
A + B = 150/25
A + B = 6 days
Thus 100% of the work is completed in 6 days,
50% of the work is completed in {(6 / 100%) * 50%} days = 3 days
9. One tap can fill the tank in 20 minutes and the other can empty in 30 minutes. If both the taps are opened in how many minutes the tank would be full
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Correct Ans:60 minutes
Explanation:
10. Two tapes can fill an empty tank in 12 and 15 minutes respectively. If both the taps are opened simultaneously in how many minutes the tank would be full.
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Correct Ans:20/3 minutes
Explanation:
Let the two taps be A and B.
Given, Tap A fill the tank in 12 mins
Tap B fill the tank in 15 mins
To find the Time taken by both taps opened together to fill the tank:
1/(A + B) = (1/A) + (1/B)
=> 1/(A + B)= (1/ 12) + (1/ 15)
=> 1/(A + B)= 27 / 180
Taking reciprocal on both sides
=> A + B = 180 / 27
=>A + B = 20 / 3 mins
11. Alan can complete a work in 10 days B is 25% more efficient than A. In how many days B and A together can complete the work.
SHOW ANSWER
Correct Ans:15 / 4 days
Explanation:
A completes in 10 days
B completes in 6 days.
A + B 1 day work = (1/10 + 1/6) = (3+5) /30 = 8 / 30 = 4 / 15
A + B can complete in 15 / 4 days
12. A can complete a job in 12 days. B is twice efficient as A, if both work together in how many days the work will get completed.
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Correct Ans:4 days
Explanation:
A can complete the work in 12 days.
B can complete the same work in 6 days.
A's 1 day work = 1/12
B's 1 day work = 1/6
A + B 's 1 day work = (1/12 + 1/6) = ( 1 + 2 ) / 12 = 3 / 12 = 1 / 4
A and B can complete the work in 4 days.
13. Two taps can fill the empty tank in 30 and 60 minutes respectively. If both the taps are opened at 7:15 AM, what time the tank will be full?
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Correct Ans:7 : 35 AM
Explanation:
14. The ratio of efficiency in completing the task of A and B is 2 : 1. If both can complete the work in 10 days, in how many days B alone can complete the work.
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Correct Ans:30
Explanation:
Given, ratio of efficiency of A and B = 2 : 1
=> which means A is twice efficient as B
=> If A completes a work in x days, then B can complete the same work in 2x days.
=> B = 2A
=> A = B/2
=> A = 0.5 B
And A + B = 10
Subs A = 0.5B and A + B = 10 in the eqn 1/(A + B) = (1/A) + (1/B)
=> 1/ 10 = (1/0.5B) + (1/ B)
=> 1/ 10 = (1 + 0.5) / 0.5B
=> 1/ 10 = 1.5 / 0.5B
Taking reciprocal on both sides
=> 10 = 0.5B / 1.5
=> 0.5B = 10 * 1.5
=> B = 15 / 0.5
=> B = 30 days
Thus, B alone can complete the work in 30 days.
15. A and B can complete a given work by working together in 8 days. B takes twice the number of days to complete the work compared to A. In how many days A can finish the work by working alone?
SHOW ANSWER
Correct Ans:12
Explanation:
Let the time taken by A to finish the work = x days
Then, time taken by B to finish the work = 2x days
Given, Time taken by A and B together ie., (A + B) = 8 days.
=>1/(A + B) = (1/A) + (1/B)
=> 1/8 = (1/x) + (1/2x)
=> 1/8 = (2 + 1) / 2x
=> 1/8 = 3/2x
Taking reciprocal on both sides,
=> 8 = 2x / 3
=> 8 * 3 = 2x
=> 24/ 2 = x
=>x = 12
A alone complete the work in 12 days.
16. Given that A and B can complete a work in 4 days, B and C can complete the same work in 6 days. If all three work together, they can complete the work in 4 days. In how many days, A and C can complete the task by working together?
SHOW ANSWER
Correct Ans:12
Explanation:
Given,A and B can complete a work in 4 days => A + B = 1/4
B + C = 1/6
A + B + C = 1/4
To find A + C = ?
W.K.T:- 2 (A + B + C) = (A + B) + (B + C) + (A + C)
=> 2 (1/4) = 1/4 + 1/6 +(A + C)
=> 1/2 =1/4 + 1/6 +(A + C)
=> 1/2 - 1/4 - 1/6 = (A + C)
On taking LCM we get,
=> (A + C) = (6 - 3 - 2) / 12
=>(A + C) = 1/12
So, A and C together can complete the work in 12 days.
17. If Ben and Charlie can complete a piece of work in 20 and 30 days respectively, then in how many days 80% of the work will get completed ?
SHOW ANSWER
Correct Ans:12
Explanation:
18. A and B can complete a work in 20 and 30 days respectively. In how many days 75% of the work will get completed?
SHOW ANSWER
Correct Ans:9
Explanation:
Let the time taken by A = 20 days
and the time taken by B = 30 days
A + B together can complete 100 % of the work in:
=>1/(A + B) = (1/A) + (1/B)
=> 1 / (A + B) = (1 / 20) + (1 / 30)
=> 1 / (A + B) = (30+ 20) / (20 * 30)
=> 1 / (A + B) = 50 / 600
Taking reciprocal on both sides
A + B = 600/50
A + B = 12 days
Thus 100% of the work is completed in 12 days,
75% of the work is completed in {(12 / 100%) * 75%} days = 9 days
19. Somu and Ramu can complete the work in 20 and 30 days respectively. In how many days, 50% of the work will get completed?
SHOW ANSWER
Correct Ans:6
Explanation:
Let the time taken by Somu= A = 20 days
the time taken by Ramu= B = 30 days
Then number of days to complete 100% of work by Somu+ Ramutogether:
=>1/(A + B) = (1/A) + (1/B)
=> 1 / (A + B) = (1 / 20) + (1 / 30)
=> 1 / (A + B) = (30 + 20) / (20 * 30)
=> 1 / (A + B) = 50 / 600
Taking reciprocal on both sides
A + B = 600/50
A + B = 12 days
Thus 100% of the work is completed in 12 days,
50% of the work is completed in {(12 / 100%) * 50%} days = 6 days
20. Ram and Shyam can complete a work in 20 and 30 days respectively. In how many days 25% of the work would have got completed ?
SHOW ANSWER
Correct Ans:3
Explanation:
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