Question

A man earns Rs 600 per month more than his wife. One tenth of a man's salary and one sixth of a wife's salary amounts to Rs 1500, which is saved every month. Find their salaries.

Answer 1

Hint: Assume that the salary of the wife be x and that of husband be x+600. Find the expression for one-tenths of man’s salary and one-sixth of wife’s salary in terms of x. Add these expressions and equate the sum to 1500. Hence form an equation in x. Solve for x. Hence find the salary of the husband and wife. Verify your answer.

Complete step-by-step answer:
Let the salary of the wife be x.
Since the salary of the man is Rs. 600 more than his wife, the salary of the man is x+600.
Hence, we have one-tenth of a man's salary is equal to ${\displaystyle \frac{x+600}{10}}$ and one-sixth of a wife's salary is equal to ${\displaystyle \frac{x}{6}}$.
Since the sum of one-tenth of man’s salary and one-sixth of wife’s salary is equal to Rs. 1500, we have
${\displaystyle \frac{x+600}{10}}+{\displaystyle \frac{x}{6}}=1500$
Multiply both sides by 30, we get
$\begin{array}{rl}& 3x+1800+5x=45000\\ & \Rightarrow 8x+1800=45000\end{array}$
Subtracting 1800 from both sides, we get
8x =43200
Dividing both sides by 8, we get
 x = 5400.
Hence the salary of the wife is Rs. 5400
Hence the salary of the man is Rs.5400+600 = Rs. 6000

Note: Verification:
Salary of man = Rs. 6000
Salar of the wife = Rs. 5400
Clearly, the salary of the man is Rs. 600 more than his wife.
Also, we have one-tenth of man’ salary $={\displaystyle \frac{6000}{10}}=600$ and one-sixth of the wife’s salary $={\displaystyle \frac{5400}{6}}=900$
Hence the sum of one-tenth of the man’s salary and one-sixth of the wife’s salary is equal to 600+900 = Rs. 1500.