A20
B16
C24
D32
Answer:
D. 32
Read Explanation:
Shortcut Trick LCM(20, 30, 24) = 120 Let work is 120u
Days | Work | Efficiency |
(A+B) 20 |
| 6 |
(B+C) 30 | 120 | 4 |
(C+A) 24 |
| 5 |
Total efficiency 2(A + B + C) = 15u
A + B + C = 7.5u
A = A + B + C - (B+C) = 7.5 - 4 = 3.5u
By same process Efficiency of B = 2.5u, C = 1.5u
B alone can complete = (120 × 2/3)/2.5 = 32 days
Given:
⇒ 1/A + 1/B = 1/20
⇒ 1/B + 1/C = 1/30
⇒ 1/A + 1/C = 1/24
Calculation:
Solving,
⇒ 1/A - 1/C = 1/20 - 1/30 = 1/60
⇒ 1/A + 1/C = 1/24
Solving,
⇒ 2/A = 1/60 + 1/24 = 7/120
⇒ 1/A = 7/240
Then,
⇒ 1/B = 1/20 - 7/240 = 1/48
B's 1 days work = 1/48
B alone can complete the work in 48 days.
∴ Time taken by B to complete 2/3rd work = 2/3 × 48 = 32 days
Alternate Method
Total work = LCM of 20, 30 and 24 = 120
In 1 day (A + B) can do 120/20 = 6 units work
In 1 day (B + C) can do 120/30 = 4 units work
In 1 day (A + C) can do 120/24 = 5 units work
In 1 day (A + C + B + C + C + A) = 2(A + B + C) can do 15 unit work
⇒ In 1 day (A + B + C) can do 15/2 = 7.5 units work
⇒ In 1 day B alone can do (A + B + C) - (A + C) = 7.5 - 5 = 2.5 units work
B alone can complete the work in 120/2.5 = 48 days
B alone can do 2/3rd part of the work in 48 × 2/3 = 32 days
∴ B alone will complete 2/3 part of the same work in 32 days.