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Q1MULTIPLE CHOICE
A alone can do a piece of work in 10 days and B alone can do it in 15 days. How long will both A and B together take to finish the same work?
Answer: A
Unitary Method:
A’s 1 day’s work =
B’s 1 day’s work =
∴(A+B)'s 1 day' s work = =
∴ Both together can finish the work in or 6 days
LCM Method:
Let the total work to be done = LCM(10, 15) = 30 units
A can complete this work in 10 days, hence A’s efficiency = 30/10 = 3 units/day
B can complete this work in 15 days, hence A’s efficiency = 30/15 = 2 units/day
Combined efficiencies of A and B = 3 + 2 = 5 units/day
Time taken by A and B together to complete the work = 30/5 = 6 days.
Hence, option (a).
Q2MULTIPLE CHOICE
A and B together can complete a piece of work in 45 days, while A alone can complete it in 60 days. So, B alone can complete the work in how many days?
Answer: D
(A+B)’s 1 day’s work = 1/45 and A’s day’s work = 1/60
Let the total work to be done = LCM(45, 60) = 180 units
A can complete this work in 60 days, hence A’s efficiency = 180/60 = 3 units/day
A and B together can complete this work in 45 days, hence their combined efficiency = 180/45 = 4 units/day
∴ B’s efficiency = 5 – 4 = 1 unit/day
Time taken by B alone to complete the whole work = 180/1 = 180 days.
Hence, option (d).
Q3MULTIPLE CHOICE
A can do a piece of work in 16 days. B is 60% more efficient than A. Find the number of days it takes B to do the same piece of work?
Answer: A
A’s 1 day’s work = ;
B is 60% more efficient than A, hence B can do 60% more work in a day than A can.
∴ B’s 1 day’s work = =
∴ B can do the work in 10 days
Hence, option (a).
Q4MULTIPLE CHOICE
A is thrice as good a workman as B and takes 20 days less to do a piece of work than B. B alone can do the whole work in:
Answer: C
Ratio of efficiency of A and B = 3 : 1.
We know the ratio of efficiency is reciprocal to the ratio of time taken to complete a certain work.
∴ Ratio of the time taken by A and B = A ∶ B ∷ 1 ∶ 3
Let A takes x days to complete the work, hence B takes 3x days to complete the same work.
⇒ 3x - x = 20
⇒ x = 10
∴ B takes 3 × 10 = 30 days.
Hence, option (c).
Q5MULTIPLE CHOICE
A can do as much work in 3 days as B can in 2 days and C can do as much work in 5 days as much work as B can in 6 days. What time will C take to complete a work that A can complete in 36 days?
Answer: D
We know the ratio of efficiency is reciprocal to the ratio of time taken to complete a certain work.
Ratio of time taken by A and B = 3 : 2
Ratio of time taken by B and C = 6 : 5
∴ Ratio of time taken by A, B and C = 9 : 6 : 5.
∴ Any work that A can complete in 36 days, C can do it in 5/9 × 36 = 20 day’s time.
Hence, option (d).
Q6MULTIPLE CHOICE
‘A’ alone can complete a piece of work in 16 days. Work done by B alone in one day is half of the work done by A alone in one day. In how many days can the work be completed, if A and B work together?
Answer: C
A can complete the work in 16 days.
Since B completes only half the work in a day as A, it means B will take twice the time than A to complete a certain work.
∴ If A can complete a certain task in 16 days, B will take 32 days to complete the same task.
∴ (A + B)’s work in 1 day = 1/16 + 1/32 = 3/32.
Hence, time taken by A and B together to complete the work = 32/3 days
Hence, option (c).
Q7MULTIPLE CHOICE
P is thrice as efficient as Q and R is twice as efficient as P. What is the ratio of the number of days taken by P, Q and R, when they work individually?
Answer: E
Ratio of efficiency of P, Q, R = 3 : 1 : 6
We know the ratio of efficiency is reciprocal to the ratio of time taken to complete a certain work.
∴ Ratio of number of days taken = 1/3 ∶ 1/1 : 1/6 = 2 ∶ 6 ∶ 1.
Hence, option (e).
Q8MULTIPLE CHOICE
Akanksha can type 20 pages in 5 minutes. Mary can type 10 pages in 10 minutes. Working together, how many pages can they type in 30 minutes?
Answer: E
Akanksha can type 20 pages in 5 minutes, hence she can type 20/5 = 4 pages per minute
Mary can type 10 pages in 10 minutes, hence she can type 10/10 = 1 pages per minute
Together, Akaksha and Mary can type 4 + 1 = 5 pages per minute.
∴ In 30 minutes they can together type = 5 × 30 = 150 pages
Alternately,
We know that Akanksha can type 20 pages in 5 minutes.
Hence, number of pages she can type in 30 mins = 20/5 × 30 = 120
We know that Mary can type 10 pages in 10 minutes
Hence, number of pages she can type in 30 mins = 10/10 × 30 = 30
Total number of pages typed by both in 30 minutes = 120 + 30 = 150
Hence, option (e).
Q9MULTIPLE CHOICE
Amit can do a work in 12 days and Sagar in 15 days. If they work on it together for 4 days, then the fraction of the work that is left is:
Answer: C
Work done by Amit in one day =
Work done by Sagar in one day =
In one day, Amit and Sagar can do = + = th
Hence, in 4 days they will complete = th of the work.
Hence, amount of work remaining after 4 days = 1 - = .
Hence, option (c).
Q10MULTIPLE CHOICE
Aakash alone can do a piece of work in 15 days. Bikash alone can do it in 24 days. They complete the work together. If the total wages for the work is Rs. 312, how much should Aakash be paid?
Answer: E
Aakash alone can do the work in 15 days.
∴ Work done by Aakash in one day = 1/15
Bikash alone can do the same work in 24 days.
∴ Work done by Bikash in one day = 1/24
When 2 or more people work for same amount of time, payment is divided in the ratio of their efficiencies. [Concept]