Question

4 men and 6 boys can finish a piece of work in 5 days while 3 men and 4 boys can finish it in 7 days. Find the time taken by 1 man alone and that by one 1 boy alone.

Answer 1

Gɪᴠᴇɴ :-

• 4M + 6B can finish a piece of work in = 5 Days.
• 3M + 4B can finish a piece of work in = 7 Days.

Tᴏ Fɪɴᴅ :-

• The time taken by 1 man alone and that by one 1 boy alone. ?

Sᴏʟᴜᴛɪᴏɴ :-

Since In Both Cases They are Doing same work.

So,

→ 5(4M + 6B) = 7(3M + 4B)

→ 20M + 30B = 21M + 28B

→ 21M - 20M = 30B - 28B

→ M = 2B

→ (M/B) = (2/1)

Hence,

→ Efficiency of a Man = 2 unit / Day.

→ Efficiency of a Boy = 1 unit / Day.

Therefore,

→ Total work = 5(4M + 6B) = 5(4*2 + 6*1) = 5(8 + 6) = 5*14 = 70 units.

So,

→ Total work done by 1 Man alone in = (70/2) = 35 Days.

→ Total work done by 1 Boy alone in = (70/1) = 70 Days.

∴ 1 Man can Finish same Piece of work alone in 35 Days & 1 can can finish it in 70 Days.

Answer 2

Given Information :

• 4 men and 6 boys can complete a work in 5 days.
• 3 men and 4 boys can finish it in 7 days.

To find :

• What is the time taken by one man alone and by one boy alone for the work to be completed ?

Solution :

Let the time taken by one man be x and the time taken by one boy be y.

Equations :

➸ 4x + 6y = 5

➸ 3x + 4y = 7

Now, we know that :

➸ Work done in one day by one man = 1/x

➸ Work done in one day by one boy = 1/y

Hence,

Equations :

➸ 4/x + 6/x = 1/5

➸ 3/x + 4/y = 1/7

Now, assuming 1/x = m and 1/y = b.

Hence,

We get :

➸ 4m + 6b = 1/5 ....(1)

➸ 3m + 4b = 1/7 ....(2)

Multiplying (1) by 3 and (2) by 4.

➸ 12m + 18b = 3/5

➸ 12m + 16b = 4/7

By elimination method,

12m + 18b = 3/5

12m + 16b = 4/7

- - -

_____________

➸ 2b = 3/5 - 4/7

➸ 2b = (21-20)/35

➸ 2b = 1/35

➸ 1 = 25 * 2b

➸ 1 = 70b

➸ b = 1/70

Hence,

➸ b = 1/y = 1/70

➸ y = 70 days

Now,

➸ 12m + 18b = 3/5

➸ 12m + 18(1/70) = 3/5

➸ 12m + 18/70 = 3/5

➸ 12m = 3/5 - 18/70

➸ 12m = (42 - 18)/70

➸ 12m = 24/70

➸ m = 24/70*1/12

➸ m = 2/70

➸ m = 1/35

Hence,

➸ m = 1/x = 1/35

➸ x = 35 days

Hence, time taken by a man to complete the task is 35 days and time taken by a boy to complete the task is 70 days.