Question

A certain sum of money is sufficient to pay either A's wage for 20 days or B's wages for 30 days. For how long will it suffice if both A and B work together?
a. 8 b. 6 c. 9 d. 5​

Answer 1

Answer:

12 days

(The answer does not seem to match the options, either options may be wrong or my solution)

Explanation:

Let the total amount be x

Since, x is sufficient to pay wage of A for 20 days

∴ Daily wage of A = x/20

Similarly, daily wage of B = x/30

When they both start working together, the combined daily wage of A and B

$=\frac{x}{20} +\frac{x}{30}$

$=\frac{x}{10} (\frac{1}{2}+\frac{1}{3} )$

$=\frac{x}{10} \times \frac{5}{6}$

$=\frac{x}{12}$

Therefore the amount x will last for = $\frac{x}{x/12}$ days

                                                           = 12 days