A can do a certain work in 12 days, and B alone can do the same work in 16…
20202020
A can do a certain work in 12 days, and B alone can do the same work in 16 days. A and B undertook to complete it for Rs. 8000. With the help of C, they completed the work in 6 days. How much money (in Rs.) should be paid to C?
- A.
1000
- B.
2000
- C.
3000
- D.
4000
Attempted by 50 students.
Show answer & explanation
Correct answer: A
Given:
A can complete the work in 12 days
B can complete the work in 16 days
Total payment = Rs. 8000
With the help of C, the work is completed in 6 days
Step 1: Find efficiencies of A and B
Efficiency of A:
= 1/12 work per day
Efficiency of B:
= 1/16 work per day
Combined efficiency of A and B:
1/12 + 1/16
Taking LCM = 48
= 4/48 + 3/48
= 7/48
Step 2: Find total efficiency with C
Since the work is completed in 6 days:
Total efficiency of A + B + C
= 1/6
Efficiency of C:
= 1/6 − 7/48
Taking LCM = 48
= 8/48 − 7/48
= 1/48
Step 3: Find C’s share of money
Total work is divided according to efficiencies.
Ratio of efficiencies:
A : B : C
= 1/12 : 1/16 : 1/48
Multiplying by 48:
= 4 : 3 : 1
Total ratio:
4 + 3 + 1 = 8
C’s share:
= (1/8) × 8000
= 1000