A & B together earn ₹840 for a job. A works the whole time; B joins after the job is 25% done. B is twice as efficient as A. Find B's share.
₹420
Wages are paid in proportion to the amount of work each person actually does.
Step 1 — set rates and total work:
Let A's rate = 1 unit/time; then B's rate = 2 units/time. Let total work = \(W\) units.
Step 2 — phase 1 (A alone, until 25% done):
A alone completes \(W/4\) at rate 1, taking time \(t_1 = W/4\).
Step 3 — phase 2 (A and B together for the remaining 75%):
Combined rate = \(1+2 = 3\) units/time. Remaining work = \(3W/4\).
\(t_2 = \dfrac{3W/4}{3} = \dfrac{W}{4}\)
Step 4 — compute each person's contribution:
A worked for the full duration \(t_1+t_2 = W/2\) at rate 1: A did \(W/2\) (50% of work).
B worked for \(t_2 = W/4\) at rate 2: B did \(2 \times W/4 = W/2\) (50% of work).
Step 5 — split the wages in this ratio:
A : B = 1 : 1, so each gets ₹420.
Hence B's share is ₹420 — option (1).
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