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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?
Explanation
This problem can be solved using the concept of rates, similar to time and work problems.
Let the total amount of money be A.
- Daily salary of R = A / 20
- Daily salary of S = A / 30
When both are paid together, their combined daily salary is the sum of their individual daily salaries:
Combined Daily Salary = A/20 + A/30
To add these fractions, we find the Least Common Multiple (LCM) of 20 and 30, which is 60:
Combined Daily Salary = (3A + 2A) / 60 = 5A / 60 = A / 12
The number of days the total amount A will last for both R and S together is:
Number of days = Total Amount / Combined Daily Salary = A / (A / 12) = 12 days
Therefore, the money is sufficient to cover both salaries for 12 days.
SIMILAR QUESTIONS
A and B together can finish a job in 20 days. B and C together can finish the same job in 30 days. If A and C together can finish it in 24 days, in how many days can A alone finish the job?
A person earns Rs. 2000 per month over and above his salary as additional charge allowance. However, 30% of this additional income will be deducted as additional income-tax at source. If the person would deposit Rs. 1000 per month on a long-term saving fetching 12% interest his tax liability on the additional allowance would reduce to 10%. What is the effective interest for this person for money invested in the long-term savings scheme ?
Suppose A and B can complete a work together in 10 days. If B alone can complete the work in 15 days, then in how many days can A alone finish the work?
'A' and 'B' have pocket money in the ratio of 3 : 4. After the day's work, 'A' earned ₹ 600 while 'B' earned ₹ 500. However, 'A' spent ₹ 150 and 'B' spent ₹ 100 during the day. If they have equal amount of money at the end of the day, then the pocket money 'A' had in the morning is: