1. Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?
SHOW ANSWER
Correct Ans:(6 / 11)
Explanation:
Given
Time taken to fill the tank by pipe A = 30 min
Time taken to fill the tank by pipe B = 20 min
Time taken to fill the tank by pipe C = 10 min
=> Part of the tank filled by pipe A in 1 minute = 1/30
Part of the tank filled by pipe B in 1 minute = 1/20
Part of the tank filled by pipe C in 1 minute = 1/10
Here we have to find the proportion of the solution R.
Pipe C discharges chemical solution R.
Part of the tank filled by Pipe C in 3 minutes = 3 * (1/10) = 3 / 10
Part of the tank filled by pipe A, B, C together in 1 minute = (1/30) + (1/20) + (1/10)
= 11 / 60
Part of the tank filled by pipe A, B, C together in 3 minutes = 3 * (11/60) = 11 / 20
Required Proportion = Part of the tank filled by Pipe C in 3 minutes / Part of the tank filled by pipe A, B, C together in 3 minutes
= (3/10) / (11/20)
= (3 * 20) / (10 * 11)
= 60 / 110
= 6 / 11
2. 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.
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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.
3. 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:
4. Two taps can fill the empty tank in 14 minutes if both are opened. Tap A alone can fill the tank in 21 minutes, in how many minutes tap B alone can fill the tank.
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Correct Ans:42
Explanation:
Given, Tap A and B fill the tank in 14 mins
=> A + B = 14 mins
Tap A alone fill the tank in 21 mins
To find the Time taken by tap B alone to fill the tank:
1/(A + B) = (1/A) + (1/B)
=> 1/14= (1/ 21) + (1/ B)
=> 1/ B = (1/14) - (1/ 21)
=> 1/ B= 7 / 294
Taking reciprocal on both sides,
=> B = 294 / 7
=> B = 42 mins
Thus, Time taken by tap B alone to fill the tank = 42 mins
5. A and B can complete the work in some days. B takes twice the number of days to complete the work compares to A. If both work together the job gets completed in 6 days. In how many days A alone can complete the work?
SHOW ANSWER
Correct Ans:9
Explanation:
Let the time taken by A = x days
Then, time taken by B = 2x days
Given, Time taken by A and B together = 6 days.
=> 1/(A + B) = (1/A) + (1/B)
=> 1/6 = (1/x) + (1/2x)
=> 1/6 = (2 + 1) / 2x
=> 1/6 = 3/2x
Taking reciprocal on both sides,
=> 6 = 2x / 3
=> 6 * 3 = 2x
=> 18 / 2 = x
=> x = 9
A alone complete the work in 9 days.
6. A and B can complete a piece of work in 12 days working together. The ratio of number of days taken to complete the work individually by A and B is 3 : 2. In how many days B alone can complete the work?
SHOW ANSWER
Correct Ans:20
Explanation:
Given, A + B = 12 days
Ratio of time taken by A and B = 3 : 2
=> A takes 3x days and B takes 2x days.
To find the time taken by “B” to complete the work:
1/ (A + B) = (1/A) + (1/ B)
=> 1/12 = (1/3x) + (1/2x)
=> 1/12 = (2 + 3) / 6x
=> 1/12 = 5 / 6x
Taking reciprocal on both sides, we get
=> 12 = 6x / 5
=> x = (12 * 5) / 6
=> x = 10
Thus, B takes 2x days = 2 * 10 = 20 days.
7. 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.
SHOW ANSWER
Correct Ans:50 %
Explanation:
8. If Ajay and Suresh can complete a piece of work in 30 and 30 days, after how many days 25 % of the work would have got completed?
SHOW ANSWER
Correct Ans:3 (3/4) days
Explanation:
Let the time taken by Ajay = A days = 30 days
the time taken by Suresh = B days = 30 days
Ajay + Suresh together can complete 100 % of the work in:
=> 1/(A + B) = (1/A) + (1/B)
=> 1 / (A + B) = (1 / 30) + (1 / 30)
=> 1 / (A + B) = 2 / 30
Taking reciprocal on both sides
A + B = 30/2
A + B = 15 days
Thus 100% of the work is completed in 15 days,
25% of the work is completed in {(15 / 100%) * 25%} days = 3.75 days (or) 3(3/4) days.
9. 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?
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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
10. 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:
11. 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
12. 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:
13. 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
14. 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:
15. 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
16. 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
17. 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.
18. 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?
SHOW ANSWER
Correct Ans:7 : 35 AM
Explanation:
19. The work efficiency of A and B are in the ratio 1: 2 and by working together they complete the work in 20 days. In how many days B can complete the work by working alone ?
SHOW ANSWER
Correct Ans:30
Explanation:
20. 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.
SHOW ANSWER
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.
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