Question

Salary of an officer increases every year by 20%. His salary in the year 2001 was Rs. 26640. What was his salary in 1999?
(a) Rs. 20, 000
(b) Rs. 19, 028
(c) Rs. 18, 500
(d) Rs. 19, 528

Answer 1

Hint: We will be using the concept of percentage change to tackle this question. His salary in 2001 is given so we will take his salary in 1999 to be x and then increase it to 20% after each year.

Complete step-by-step answer:
Let the salary of an officer in the year 1999 be Rs. \[x\] .

So now let his salary in 2000 after an increment of 20% be Rs. \[y\],

 \[y=x+20\%\times x........(1)\]

Now changing the 20% into fraction in equation (1) we get,

 \[y=x+\dfrac{20}{100}\times x\]

 \[y=x+\dfrac{1}{5}\times x\]

Now taking the LCM and then adding it we get,

 \[y=\dfrac{6x}{5}........(2)\]

His salary in 2001 is mentioned in the question and it is Rs. 26640 and hence the 20% increment in the salary of year 2000 will be equal to Rs. 26640. And the salary in 2000 after an increment of 20% is \[y\]. So we get,

 \[\Rightarrow y+20\%\times y=26640\]

Now substituting value of y from equation (2) we get,

 \[\Rightarrow \dfrac{6x}{5}+20\%\times \dfrac{6x}{5}=26640...........(3)\]

Changing 20% into fraction in the equation (3) we get,

 \[\Rightarrow \dfrac{6x}{5}+\dfrac{20}{100}\times \dfrac{6x}{5}=26640..........(4)\]

Solving equation (4) we get,

 \[\begin{align}

  & \Rightarrow \dfrac{6x}{5}+\dfrac{1}{5}\times \dfrac{6x}{5}=26640 \\

 & \Rightarrow \dfrac{6x}{5}+\dfrac{6x}{25}=26640 \\

\end{align}\]

After taking LCM we get,

 \[\Rightarrow \dfrac{36x}{25}=26640\]

Now bringing all the numbers to one side and the variable x to another side we get,

 \[\Rightarrow x=\dfrac{26640\times 25}{36}=18500\]

Hence the answer is that in the year 1999 his salary was 18, 500. So option (c) is the right option.

Note: Whatever the question is asking us to find we will take it to be x, this way it consumes less time. We can make a mistake by not adding y to the 20% increment in y and only equating the increment in y to 26640.