- 6 days
- 5 days
- 4 days
- 3 days
Call
Option 1 : 6 days
Given:
20 men and 30 women can do a piece of work in 5 days
10 men and 25 women can do a piece of work in 9 days
Concept used:
If a person does work in ‘n’ days then, one day of work by a person is 1/n part of work.
Calculation:
1 day work by 20 men and 30 women = 1/5 part of the work
1 work done in one day required = 20 × 5 men + 30 × 5 women
⇒ 1 work done in one day required = 100 men + 150 women ----(i)
1 day work by 10 men and 25 women = 1/9 part of the work
1 work done in one day required = 10 × 9 men + 25 × 9 women
⇒ 1 work done in one day required = 90 men + 225 women ----(ii)
From equation (i) and equation (ii)
100 men + 150 women = 90 men + 225 women
⇒ 100 men – 90 men = 225 women – 150 women
⇒ 10 men = 75 women
And 1 work by 20 men and 30 women = 5 days
⇒ 1 work by (75 women × 2) + 30 women = 5 days
⇒ 1 work by 150 women + 30 women = 5 days
⇒ 1 work by 180 women = 5 days
Now from question, 20 men = 2 × 75 women
⇒ 150 women
But 180 women = 5 days
⇒ 1 woman does one work in = 5 × 180 days
⇒ 150 women does a work in = 5 × 180/150 days
⇒ 180/30 days
⇒ 6 days.
∴ The time taken by 20 men for work is 6 days.
Talk Doctor Online in Bissoy App