Question

The employer reduces the number of employees in the ratio 9 : 8 and increases their wages in the ratio 14 : 15 .If the previous wage bill was Rs 189000 what is the amount by which the new wage bill will increase or decrease \[\]
A.Rs. 21000\[\]
B.Rs. 10000\[\]
C.Rs.9000\[\]
D.Rs. 250000\[\]

Answer 1

Hint: We assume the number of employees before and after reduction in numbers as $9x$ and $8x$. We find the wage of $8x$ employees using the old wage bill. We assume the wages of $8x$ employees before the increment in wage as $14y$ and after as$15y$. We find new wage bill and see by how much it has increased or decreased from old wage bill by subtraction.\[\]

Complete step by step answer:
We are given the question that the employer reduces the number of employees in the ratio 9: 8 and increases their wages in the ratio 14: 15. Let us assume the number of employees before the reduction in number of employees as $9x$ then the number of employees after the reduction in number of employees is $8x$. \[\]
We are further given in the question that the previous wage bill was Rs 189000 which means sum of the wages of $9x$ employees was Rs. 189000. So we have;
\[\Rightarrow 9x=189000\]
 We divide both side of the above equation by 9 to have;
\[\Rightarrow x=21000\]
So the sum of the wages of $8x$ employees after the reduction in number of employees in rupees is;
\[\Rightarrow 8x=8\times 21000=168000\]
We are also given in the question that increases wages of $8x$ employees in the ratio 14: 15. Let us assume the wage of an employee before and after the increment as $14y$ and $15y$. The wage bill of $14y$ employees before the increment was 168000 rupees as obtained before. So we have;
\[\Rightarrow 14y=168000\]
We divide both side of the above equation by 14 to have;
\[\Rightarrow y=12000\]
So the wage bill after the increment in wages of $15y$ employees in rupees is;
\[15y=15\times 12000=180000\]
So the new wage bill after the reduction in employees and increment in wages is 180000 rupees and the old wage bill was 189000 rupees. So the amount by which the wage bill has increased is
\[\text{New wage bill}-\text{old wage bill}=189000-18000=9000\]

So, the correct answer is “Option C”.

Note: We note that if we multiply a positive number $k$ to positive number the ratio will not change which means $a:b=ka:kb$. We compare change in change in quantities either using ratio or percentage. We must be careful of the mistake of calculating wage difference between new wage bill Rs.180000 and sum of the wages of $8x$ employees before the increment Rs.168000 as the answer.