P can do a piece of work alone in 16 days, Q can do the same work alone in 24 days, while R can do it alone in 48 days. They work together and complete the work, and receive a total of ₹744 as payment for doing the work. What is the share of the person who received the smallest amount?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. ₹124.
Concept Used :
Total work = Number of days × efficiency
Given:
P alone can do the work in 16 days.
Q alone can do the work in 24 days and
R alone can do the work in 48 days.
Explanation:
Now, let the total work be LCM of (16, 24, 48) = 48 units.
So, efficincy of P = 48/16 = 3 units/day
Efficiency of Q = 48/24 = 2 units/day
Efficiency of R = 48/48 = 1 unit/day
Let the amount recieved by P, Q, R be 3x, 2x, x respectively.
The total amount recieved = ₹744
⇒ (3x + 2x + x) = 744
⇒ 6x = 744
⇒ x = 124.
Hence the person who recieved the smallest amount is x = ₹124.