Question

किसी कार्य को A अकेला 16 दिनों में तथा B अकेला 12 दिनों
में पूरा कर सकता है। A से शुरू करते हुए वे एकान्तर दिनों पर
कार्य करते हैं। सम्पूर्ण कार्य कितने दिनों में पूरा होगा?​

Answer 1

English Translation:

A alone can complete a work in 16 days, and B alone in 12 days. Starting with A, they work on alternate days. The total work will be completed in.

The total work will be completed in 55/4 days.

Given:

A alone complete a work in 16 days

B alone complete a work in 12 days

To find:

the total work will be completed in

Solutions:

A’s 1 day of work = 1/16 units

B’s 1 day of work=  1/12 units

⇒ As they are working on alternate days

So their 2 days of work = (1/16 + 1/12) units

⇒ (7/48) units

Now, we can find the work done in 6 pairs by multiplying 6 with the 1-pair of work.

Thus, we get,

⇒ 6 * (7/48) = 42/48 units

Thus, the number of units obtained has been the work done in 12 days.

Now, only 6 units of work remain to be done.

Now, we will evaluate the value of the remaining work.

Thus, we get,

⇒ 1- 42/48

⇒6/48 units.

Now, we will find the work done on the 13th day as it’s A’s turn, and A does 1/16 of the whole work in 1 day.

Thus, the remaining work is 48(1/16)= 3 units

Now, we will find the number of days 3 units of work will take.

As B comes the next day, on the 14th day, we will find the number of units of work.

That is,

⇒1/12 *(48)= 4 units

As only 3 unit of work is required to be completed, b will take 3/4 days to complete the remaining 3 unit of work.

Hence, the total number of days the work gets to be completed

= 12 + 1 + 3/4

⇒ 13 + 3/4

⇒ 55/4 days

#SPJ1