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?
[amp_mcq option1=”12 days” option2=”15 days” option3=”11 days” option4=”20 days” correct=”option1″]
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.