An amount is adequate to pay salaries to R for 20 days or to S for 30 days. For how many days is the money enough to cover salaries of both of them together?
12 days
15 days
11 days
20 days
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CISF-AC-EXE – 2024
Let the total amount of money (representing the total work) be M.
R can be paid for 20 days with M. So, R’s daily salary (work rate) = M/20 per day.
S can be paid for 30 days with M. So, S’s daily salary (work rate) = M/30 per day.
If both R and S are paid together, their combined daily salary is R’s daily salary + S’s daily salary = M/20 + M/30.
To find how many days (let’s call this D) the money M will last for both, we set M equal to the combined daily salary multiplied by D:
M = (M/20 + M/30) * D
Divide both sides by M (assuming M > 0):
1 = (1/20 + 1/30) * D
Find a common denominator for 1/20 and 1/30, which is 60:
1/20 + 1/30 = 3/60 + 2/60 = 5/60 = 1/12.
So, 1 = (1/12) * D
Multiply by 12 to find D:
D = 12 days.