Question

प्रश्न- A और B एक काम को मिलकर 38 दिन में कर सकते हैं। वे एक साथ मिलकर काम करना शुरू करते हैं, लेकिन काम समाप्त होने से 12 दिन पहले ही A को काम छोड़ना पड़ता है और इसलिए काम पूरा समाप्त करने में उन्हें कुल 45 दिन लगे। A अकेला उसी कार्य को कितने दिन में कर सकता है?

Que.- A and B together can complete a work in 38 days. They start working together, but A has to leave 12 days before the work is over and hence it takes them a total of 45 days to finish the work. In how many days A alone can do the same work.
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Answer 1

Given :- A and B together can complete a work in 38 days. They start working together, but A has to leave 12 days before the work is over and hence it takes them a total of 45 days to finish the work. In how many days A alone can do the same work. ?

Solution :-

→ Per day work of (A + B) = (1/38) unit .

Now, we have given that, A leaves 12 days before the work is over, that means, in last 12 days only B completes the work .

Also, total work completed in 45 days . That means (45 - 12 = 33 days (A + B) work together .)

A/q,

→ 33(A + B) + 12B = 1

→ 33(1/38) + 12B = 1

→ (33/38) + 12B = 1

→ 12B = 1 - (33/38)

→ 12B = (5/38)

→ B = (5/38*12)

→ B = (5/456)

therefore,

→ A alone can complete the work in = (1/38) - (5/456) = (12 - 5)/456 = (7/456) = (456/7) = 65(1/7) days. (Ans.)

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Answer 2

Given :- A and B together can complete a work in 38 days. They start working together, but A has to leave 12 days before the work is over and hence it takes them a total of 45 days to finish the work. In how many days A alone can do the same work. ?

Solution :-

→ Per day work of (A + B) = (1/38) unit .

Now, we have given that, A leaves 12 days before the work is over, that means, in last 12 days only B completes the work .

Also, total work completed in 45 days . That means (45 - 12 = 33 days (A + B) work together .)

A/q,

→ 33(A + B) + 12B = 1

→ 33(1/38) + 12B = 1

→ (33/38) + 12B = 1

→ 12B = 1 - (33/38)

→ 12B = (5/38)

→ B = (5/38*12)

→ B = (5/456)

therefore,

→ A alone can complete the work in = (1/38) - (5/456) = (12 - 5)/456 = (7/456) = (456/7) = 65(1/7) days. (Ans.)

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