A can complete a work in 14 days while B can do it in 20 days. They started working together but after some days. A Left the work and the whole work will complete in 10 days, Find after how many days A left the work?

Question

A can complete a work in 14 days while B can do it in 20 days. They started working together but after some days. A Left the work and the whole work will complete in 10 days, Find after how many days A left the work?

10 days
9 days
7 days
5 days

LohaHridoy

9 views

2025-01-04 04:42

1 Answers

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

Option 3 : 7 days

Given:

A can complete the work in 14 days

B can complete the work in 20 days

A + B together work for some days and then A left

Total work completed in 10 days

Calculation:

A = 14 days

B = 20 days

Total work = LCM(14,20) = 140 unit

⇒ One day's work of A = 140/14 = 10

⇒ One day's work of B = 140/20 = 7

Let A and B worked together for X days, and then A left

⇒ B alone worked for (10 - X) days

Total work = ((10 + 7) × X) + (7 × (10 - X)) = 140

(17 × X) + 70 - (7 × X) = 140

(17 × X) - (7 × X) = 140 - 70

10 × X = 70

X = 7

⇒ A and B worked together for 7 days and then A left

∴ A left after 7 days

Shortcut Trick

LCM of A and B is 140

The efficiency of A = 10

The efficiency of B = 7

B worked for 10 days

= 7 × 10 = 70

Remaining work done by A

= (140 - 70)/10 = 7 days.

∴ A left after 7 days