Page 141 - Maths Skills - 8

Direct and Inverse Proportions 139

Let us learn through examples.

Let’s Attempt

Example 1: Happy can paint a house in 15 days and Anoop can paint the same house in 20 days. If they work
together, in how many days will the house be painted?
Solution: Happy can paint the house in 15 days.

Happy’s 1 day work = 1
15
Anoop can paint the house in 20 days.
Anoop’s 1 day work = 1
20
Happy’s and Anoop’s 1 day work = 1 + 1 = 43+ = 7
15 20 60 60
If Happy and Anoop work together, 7 of the work is completed in 1 day.
60
4
The whole work will be completed in 1÷ 7 days = 1× 60 = 8 days.
60 7 7
4
Hence, Happy and Anoop can together paint the house in 8 days.
7
Example 2: X can do a piece of work in 30 days and Y can finish it in 25 days. They work together for
10 days and then X leaves. In how many days will Y finish the remaining work?

Solution: X’s 1 day’s work = 1
30
1
Y’s 1 day’s work =
25

So, (X + Y)’s 1 day’s work =  1 + 1   = 11 ·
 30 25 150

(X + Y)’s 10 day’s work = 10 × 11 = 11 .
150 15
 11 4
The remaining work = 1− 15  = 15


Now, Y can do the whole work in 25 days.

Y can do 4 work in 25 × 4 = 20 days.
15 15 3
2
Hence, the remaining work is done by Y in 6 days.
3
Example 3: Manav and Aditya can do a piece of work in 6 days. Manav alone can do the same piece of work in
30 days. Find the number of days in which Aditya alone can complete the work.

Solution: Manav and Aditya can do a work in 6 days.

Manav’s and Aditya’s 1 day work = 1
6
Manav alone can do the work in 30 days.

Manav’s one day work = 1
30