Question

P and r complete a work in 10 days doing together.if p works for 2.5 days and r for 8.5 days,they finish half work.in how much time p alone complete the work ? shortcut batao iska

Answer 1

Let the number of days taken by p be P and number of days by r be R.

In one day they can do :

1/10 of the work.

In how many days can they do 1/2 of the work?

1/2 × 10/1 = 5days.

We will have two equations as follows.

In one day :

P does = 1/P

r does = 1/R

In 2.5 days P does :

2.5/P

In 8.5 days r does :

8.5/R

Total is :

(2.5/P + 8.5/R) × 5 = 0.5............. 1

(1/P + 1/R) × 10 = 1.. ........ 2

From 1:

12.5/P + 42.5/R = 0.5

12.5R + 42.5P = 0.5PR

0.5PR - 42.5P = 12.5 R

P(0.5R - 42.5) = 12.5 R

P = 12.5R / (0.5R - 42.5)

Substituting this in 2 we have :

10/(12.5R /(0.5R - 42.5) + 10/R = 1

10(0.5R - 42.5) / 12.5R + 10/R = 1

10R(0.5R - 42.5) + 10 × 12.5R = 12.5R × R

5R² - 425R + 125R = 12.5R²

5R² - 300R = 12.5R²

12.5 R² - 5R² = - 300R

-300R = 7.5R²

R = 300/7.5 = 40 days

10/P + 10/40 = 1

400 + 10P = 40P

30P = 400

P = 13 1/3 days

Answer 2

10( p + r) = ( 2.5 p + 8.5 r) x2

5p = 7r

P/r = 7/5

Total work = 10(7 + 5) = 120


Time for p = 120/7