Question

2 men and 3 boys together can do a piece of work
in 8 days. The same work is done in 6 days by
3 men and 2 boys together. How long would 1 boy
alone and 1 man alone take to complete the work
independently?
(1) 40 days, 120 days
(2) 120 days, 40 days
(3) 20 days, 120 days
(4) 120 days, 20 days​

Answer 1

Answer:

20 day, 120 days

Step-by-step explanation:

Let the no. of days taken by men be 'x' and thatby boys be 'y'.

According to the conditions given,

the eq can be written as follows...

2/x + 3/y = 1/8.

3/x +2/y = 1/6.

Substitute 1/x = a and

1/y = b

therefore,

2a+3b = 1/8. ... (1)

3a+4b = 1/6. ....(2)

Since we need the denominator as 1

So multiply eq. 1 by 8 and eq. 2 by 6

this way we get the following eqs.

16a + 24b = 1. ...(3)

18a + 12b = 1. ...(4)

Subtract eq.3 and 4,

16a + 24b = 1

- 18a + 12b = 1

-2a +12b = 0

2a = 12b

a = 6b. ...(5)

Substitute eq. 5 in eq.3

16(6b) + 24b = 1

96b + 24b = 1

120b = 1

b = 1/120

substitute the value of b in eq. 4

18a + 12 × 1 /120 = 1

18a + 1 / 10 = 1

18a = 1 - 1/ 10

18a = 9/10

a = 9/10 × 1/18

a = 1/10 × 1/2

a = 1/20

Let's replace the values of a and b

a = 1/20 = 1/x

therefore, x = 20

b = 1/120 = 1/y

therefore, y = 120.