Question

A, B तथा C एक काम को क्रमश: 10, 12 और 15 दिनों में समाप्त कर सकते हैं। यदि 'B' 2 दिन काम करके छोड़ दे, तो शेष काम A और C कितने दिनों में समाप्त करेंगे।​

Answer 1

Given

A can complete the work in 10 days.

B can complete the work in 12 days.

C can complete the work in 15 days.

B works only 2 days .

To find :-

In how many days the remaining work will be completed after leaving B .

Solution :-

The total amount of work is 1.

A can do work in 1 day = 1/10

B can do work in 1 day = 1/12

C can do work in 1 day = 1/15

→ Work done by B in 2 days = (1/12).2

→ So B did 1/6 th part of work .

Work left for A and C = 1 - 1/6

→ 5/6 th part of work.

Work done by A and C together in starting 2 days = 2/10 + 2/15 = 1/3rd part.

Now After 2 days remaining work= 5/6 - 1/3

→ 1/2 nd part of work is left for A and C.

A+C. = 1/10 + 1/15 = 1/6

They both can do 1/6 th part of work in a day .

So 1/2 part of work will complete in = (1/2)/(1/6) days

→ 3 days .

So The remaining work will be completed by A and C in 3 days

Answer 2

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$\huge\tt{GIVEN:}$

• A could complete a work in 10 days
• B could complete a work in 12 days
• C could complete a work in 15 days
• B works only 2 days.

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$\huge\tt{TO~FIND:}$

• In how many days the remaining work would be done as well as B have lefted.

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$\huge\tt{SOLUTION:}$

Let the total amount of work be 1 unit

Then,

A = 1/10 of a unit

B = 1/12 of a unit

C = 1/15 of a unit

↪work by B in 2 days = 1/12th × 2

↪work done be B = 1/6 th unit

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Work left for A & C = 1-(1/6) or 5/6 of the work

Then,

Work done by A & C in first 2 days = (2/10 +2/15)of the unit or ⅓ of the work

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Now, left work after these two days,

↪Left work = 5/6 - 1/3

↪Left work = ½ of a unit

They both can do 1/6 of a unit in a day

so,

↪½ of the work would be completed in = (½)÷(1/6)

↪½ of the work would be completed in = 3 Days

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Hence,

The remaining work would be done in 3 Days.

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