Question

A computer costs \[Rs\,39600\] . In the last $6$ months, the price had come down by $12$ percent. What was the price of the computer six months back?

Answer 1

Hint: The given questions revolve around the concepts of percentages and profit and loss. The question requires us to find the price of a computer $6$ months ago given the reduction percentage and the latest price. Such questions require accuracy in arithmetic. We will also have to use a transposition method to solve this particular question.

Complete step by step solution:
So, we are given that,
Cost of the price of computer $ = Rs\,39600$
Percentage reduction in price $ = 12\% $
Now, we have to calculate the price of the computer $6$ months back. So, let us assume that the price of the computer $6$ months back was Rs x.
Now, we have to reduce this price by $12$ percent so as to calculate the price of the computer now which is already given to us as \[Rs\,39600\] .
Hence, the reduction in price of the computer $ = \dfrac{{12}}{{100}}x$
Now, new price of the computer$ = x - \dfrac{{12}}{{100}}x = \dfrac{{88}}{{100}}x$
So, we get,
 \[\dfrac{{88}}{{100}}x = Rs\,39600\]
Now, we will solve this algebraic equation with the help of transposition rules. Method of transposition involves doing the exact same mathematical thing on both sides of an equation with the aim of simplification in mind. So, multiplying both the sides of the equation with $\dfrac{{100}}{{88}}$, we get,
 \[ \Rightarrow x = Rs\,39600 \times \dfrac{{100}}{{88}}\]
Cancelling the common factors in numerator and denominator, we get,
 \[ \Rightarrow x = Rs\,450 \times 100\]
Simplifying the calculations further, we get,
 \[ \Rightarrow x = Rs\,45000\]
So, the price of the computer six months back \[Rs\,45000\]
So, the correct answer is “ \[Rs\,45000\]”.

Note: If we add, subtract, multiply or divide by the same number on both sides of a given algebraic equation, then both sides will remain equal. Work as many problems as possible to crack these types of problems in a limited time period.