Riya and Sangeeta can finish a work in 6 days and 8 days, respectively. Riya started the work alone and then after 3 days, Sangeeta joined Riya. They both finish the remaining work. How long did the total work last?

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Question

This question was previously asked in

SSC CHSL Exam 2024 Tier-I Official Paper (Held On: 03 Jul, 2024 Shift 4)

Answer 1

Given:

Riya can finish the work in 6 days.

Sangeeta can finish the work in 8 days.

Riya worked alone for 3 days, then Sangeeta joined her.

Formula Used:

Work Rate = 1 / Number of days to complete work

Total Work = Work Rate × Time

Calculation:

Riya's work rate = 1/6

Sangeeta's work rate = 1/8

Work done by Riya in 3 days = 3 × (1/6) = 1/2

Remaining work = 1 - 1/2 = 1/2

Combined work rate of Riya and Sangeeta = 1/6 + 1/8

Combined work rate = (1)/(6) + (1)/(8) = (4 + 3)/(24) = (7)/(24)

Time taken to finish the remaining work = Remaining work / Combined work rate

Time taken = (1/2)/(7/24) = (1)/(2) × (24)/(7) = (24)/(14) = (12)/(7)

Total time = Time Riya worked alone + Time taken to finish the remaining work

Total time = 3 + (12)/(7) = (21)/(7) + (12)/(7) = (33)/(7) = 4 (5)/(7)

The total work lasted \(4 \frac{5}{7}\) days.

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