Anuj, Bibhuti and Chandu can lay 432 m of wires together in 8 days. In a day,…
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Anuj, Bibhuti and Chandu can lay 432 m of wires together in 8 days. In a day, Chandu can lay as many more meters of wire than Bibhuti as Bibhuti can lay more than Anuj. Chandu’s 5 days of work is equivalent to Anuj’s 7 days of work. How many meters of wire can Anuj alone lay in a day?
- A.
9 m
- B.
15 m
- C.
18 m
- D.
21 m
Attempted by 12 students.
Show answer & explanation
Correct answer: B
Key idea: the three rates form an arithmetic progression with Bibhuti as the middle term.
Step 1: Find combined daily work.
They lay 432 m in 8 days, so together per day = 432 ÷ 8 = 54 m. Therefore the average per person = 54 ÷ 3 = 18 m.
Step 2: Use arithmetic progression and given condition.
Let Bibhuti = 18 m/day (middle term). Then let Anuj = 18 - x and Chandu = 18 + x.
Given: 5 days of Chandu’s work = 7 days of Anuj’s work, so 5(18 + x) = 7(18 - x).
Step 3: Solve the equation.
5(18 + x) = 7(18 - x) ⇒ 90 + 5x = 126 - 7x ⇒ 12x = 36 ⇒ x = 3.
Therefore Anuj = 18 - x = 18 - 3 = 15 m/day.