p and r does a work in 10 days p does only 2.5 day and r does only 8.5 day so half work done. in how many days p will done the work.
Answers
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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