An employer reduces the number of his employees in the ratio of 5 : 4 and increases their wages in the ratio of 7 : 8. Find the ratio in which the wage bill increases or decreases due to this change. Also find the difference if the bill was Rs.490 earlier.a.Rs.532b.Rs.50c.Rs.42d.Rs.448
Question
An employer reduces the number of his employees in the ratio of 5 : 4 and increases their wages in the ratio of 7 : 8. Find the ratio in which the wage bill increases or decreases due to this change. Also find the difference if the bill was Rs.490 earlier.a.Rs.532b.Rs.50c.Rs.42d.Rs.448
Solution
The problem involves two ratios: the ratio of the reduction in employees (5:4) and the ratio of the increase in wages (7:8).
Step 1: Understand the ratios The first ratio means that for every 5 employees before, there are now 4. The second ratio means that for every 7 units of wage before, it is now 8 units.
Step 2: Calculate the new wage bill ratio The total wage bill is calculated by multiplying the number of employees by their wages. So, the ratio of the old wage bill to the new wage bill is (57) : (48) = 35 : 32.
Step 3: Calculate the difference in wage bill The wage bill has decreased in the ratio 35:32. If the wage bill was Rs. 490 earlier (corresponding to 35 in the ratio), we need to find the value corresponding to 32 in the ratio.
We can set up a proportion to solve for this: 35/490 = 32/x Solving for x gives us x = (490 * 32) / 35 = Rs. 448
Step 4: Find the difference The difference in the wage bill is Rs. 490 - Rs. 448 = Rs. 42
So, the wage bill decreases in the ratio 35:32 and the difference is Rs. 42. The correct answer is c. Rs. 42.
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