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Question 1 of 5
1. Question
Ankush, Prahlad and Charan are working on a project. Prahlad and Charan together are twice efficient as Ankush working alone. Ankush and Charan together are 4 times efficient as Prahlad working alone. In how many days Charan can complete the project alone if Prahlad completes it in 21 days?
Correct
Answer: Option (b)
Explanation:
Efficiency of Ankush = A
Efficiency of Prahlad = B
Efficiency of Charan = C
Given,
B + C = 2A … (1)
A + C = 4B … (2)
Solving (1) & (2), by eliminating A
3C = 7B
Thus, B : C = 3 : 7
(B/C) = (3/7) = (21/x)
x = 49
Incorrect
Answer: Option (b)
Explanation:
Efficiency of Ankush = A
Efficiency of Prahlad = B
Efficiency of Charan = C
Given,
B + C = 2A … (1)
A + C = 4B … (2)
Solving (1) & (2), by eliminating A
3C = 7B
Thus, B : C = 3 : 7
(B/C) = (3/7) = (21/x)
x = 49
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Question 2 of 5
2. Question
Dheeraj was supposed to build a bridge in 86 days. During construction he deployed 234 men, each working 18 hours a day. After 60 days, 3/7 of the work is completed. How many additional men should be employed by him, so that the work may be completed in time If from now on each man works for 20 hours a day?
Correct
Answer: Option (d)
Explanation:
Let us assume that M1 men can complete W1 work in D1 days, while working H1 hours per day.
Similarly, let us assume that M2 men can complete W2 work in D2 days, while working H2 hours per day.
Then, (M1D1H1)/W1 = (M2D2H2)/W2
Here, M1 = 234, D1 = 60, H1 = 18, W1 = 3/7
M2 = (234 + x), D2 = (86 – 60) = 26, H2 = 20, W2 = (1 – 3/7) = 4/7 (x is the extra men employed)
Now let us apply the formula:
(M1D1H1)/W1 = (M2D2H2)/W2
Or (234 × 60 × 18)/(3/7) = (234 + x) × 26 × 20/(4/7)
Or (234×60×18×4)/(3×26×20) = 234 + x
Or 648 = 234 + x
Or x = 648 – 234
Or x = 414
Therefore, required additional men = 414. Hence, option (d) is the correct answer
Incorrect
Answer: Option (d)
Explanation:
Let us assume that M1 men can complete W1 work in D1 days, while working H1 hours per day.
Similarly, let us assume that M2 men can complete W2 work in D2 days, while working H2 hours per day.
Then, (M1D1H1)/W1 = (M2D2H2)/W2
Here, M1 = 234, D1 = 60, H1 = 18, W1 = 3/7
M2 = (234 + x), D2 = (86 – 60) = 26, H2 = 20, W2 = (1 – 3/7) = 4/7 (x is the extra men employed)
Now let us apply the formula:
(M1D1H1)/W1 = (M2D2H2)/W2
Or (234 × 60 × 18)/(3/7) = (234 + x) × 26 × 20/(4/7)
Or (234×60×18×4)/(3×26×20) = 234 + x
Or 648 = 234 + x
Or x = 648 – 234
Or x = 414
Therefore, required additional men = 414. Hence, option (d) is the correct answer
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Question 3 of 5
3. 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 42 days?
Correct
Answer: Option (b)
Explanation:
Ratio of time taken is inversely proportional to the efficiency.
Ratio of time taken by A and B = 100 : 130 = 10 : 13
Suppose B takes x days to do the work.
Then, 10 : 13 :: 42 : x
Or x = [42 × (13/10)]
Or x = 546/10
A’s 1 day’s work = 1/42
B’s 1 day’s work = 10/546
(A + B)’s 1 day’s work = (1/42 + 10/546) = [(13 + 10)/546] = 23/546
Therefore, A and B together can complete the work in (546/23), i.e. 23.74 days.
Now, 23.74 days is more than 20 days. Hence, option (b) is the correct answer.
Incorrect
Answer: Option (b)
Explanation:
Ratio of time taken is inversely proportional to the efficiency.
Ratio of time taken by A and B = 100 : 130 = 10 : 13
Suppose B takes x days to do the work.
Then, 10 : 13 :: 42 : x
Or x = [42 × (13/10)]
Or x = 546/10
A’s 1 day’s work = 1/42
B’s 1 day’s work = 10/546
(A + B)’s 1 day’s work = (1/42 + 10/546) = [(13 + 10)/546] = 23/546
Therefore, A and B together can complete the work in (546/23), i.e. 23.74 days.
Now, 23.74 days is more than 20 days. Hence, option (b) is the correct answer.
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Question 4 of 5
4. Question
Ravish can complete a work in 60 days and Somu can complete the same work in 5 days more than the number of days in which they both can complete work together. They both start the work and after 5 days, Ravish leaves and Somu starts working with 4/3 times efficiency as before. In how much time the work will be completed?
Correct
Answer: Option (d)
Explanation:
Let they both complete work together in x days
So Somu can do it in (x+5) days
So 1/60 + 1/(x+5) = 1/x
Solve, x = 15, So Somu can complete work in 20 days
Now they work for 5 days so completed work= (1/60 + 1/20) × 5 = 1/3 of work
Remaining work = 2/3.
Somu works with 4/3 times efficiency.
So now he can complete whole work in 20/(4/3) = 15 days
So he can complete 2/3 of the work in 2/3 × 15 = 10 days
So total number of days = 5 + 10 = 15 Hence option (d) is correct answer.
Incorrect
Answer: Option (d)
Explanation:
Let they both complete work together in x days
So Somu can do it in (x+5) days
So 1/60 + 1/(x+5) = 1/x
Solve, x = 15, So Somu can complete work in 20 days
Now they work for 5 days so completed work= (1/60 + 1/20) × 5 = 1/3 of work
Remaining work = 2/3.
Somu works with 4/3 times efficiency.
So now he can complete whole work in 20/(4/3) = 15 days
So he can complete 2/3 of the work in 2/3 × 15 = 10 days
So total number of days = 5 + 10 = 15 Hence option (d) is correct answer.
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Question 5 of 5
5. Question
X and Y working together can finish a job in T days. If X works alone and completes the job, he will take T + 5 days. If Y works alone and completes the same job, he will take T + 45 days. What is T?
Correct
Answer: Option (c)
Explanation:
X’s one day’s work = 1/(T + 5)
Y’s one day’s work = 1/(T + 45)
(X + Y)’s combined one day’s work = 1/T
1/(T + 5) + 1/(T + 45) = 1/T
Solving, T = 15 days. Hence, option (c) is the correct answer.
Incorrect
Answer: Option (c)
Explanation:
X’s one day’s work = 1/(T + 5)
Y’s one day’s work = 1/(T + 45)
(X + Y)’s combined one day’s work = 1/T
1/(T + 5) + 1/(T + 45) = 1/T
Solving, T = 15 days. Hence, option (c) is the correct answer.
