If Jaya and Shushma together can complete a given task together in 40 days. They started working together but Jaya left the job after working for 15 days, and the remaining job was done by Shushma in 40 days, then in how many days Shushma can complete the whole work alone?

Question

If Jaya and Shushma together can complete a given task together in 40 days. They started working together but Jaya left the job after working for 15 days, and the remaining job was done by Shushma in 40 days, then in how many days Shushma can complete the whole work alone?

64 days
72 days
80 days
56 days

LohaHridoy

6 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 1 : 64 days

Given:

Jaya and Shushma can complete the work together in 40 days

Jaya worked for 15 days with Sushma and left afterwards

The remaining work is done by Shushma in 40 days

Concept used

If a person does the work in x days then work done by the person in 1 day = 1/x of total work.

Calculation:

Work completed by Jaya and Shushma together in 1 day = 1/40

Work completed by them in 15 days = 15/40 = 3/8

Remaining work = 1 – 3/8 = 5/8

According to the question, Shushma can complete 5/8 work in 40 days

Shushma can complete 1 work in 40 × 8/5 = 64 days

∴ Shushma can complete the whole work alone in 64 days

Shortcut Trick

Formula used:

M₁D₁ = M₂D₂

Here, M and D are the person who is working and time taken respectively

Time = Total work/Efficiency

Calculation:

Now, According to question,

Considering the first letter of Jaya and Shushma as their respective unit work

(J + S) × 40 = (J + S) × 15 + 40S

⇒ (J + S) × 25 = 40S

⇒ 25J = 15S

⇒ J = (3/5)S

Time is taken to do work alone by Shushma = {(J + S) × 40}/S

= {((3/5)S + S) × 40}/S

= (8/5) × 40

= 64

∴ Shushma can complete the whole work alone in 64 days