Question

The number $ 12,000 $ is first decreased by $ 25\% $ and then increased by $ 25\% $ Find the resulting number.

Answer 1

Hint: Here first of all we will frame the equation for the resulting value decreasing the given percentage and increasing the given percentage and then simplify for the resultant required value.

Complete step-by-step answer:
Percentage is expressed as the fraction with the denominator hundred.
The resulting value $ = $ the original number $ \times \left( {1 - \dfrac{{25}}{{100}}} \right) \times \left( {1 + \dfrac{{25}}{{100}}} \right) $
Place the given original number in the above expression and simplify the expression taking LCM(least common multiple)
The resulting value $ = 12000 \times \left( {\dfrac{{100 - 25}}{{100}}} \right) \times \left( {\dfrac{{100 + 25}}{{100}}} \right) $
Simplify the above expression finding the respective sum and difference of the terms.
The resulting value $ = 12000 \times \left( {\dfrac{{75}}{{100}}} \right) \times \left( {\dfrac{{125}}{{100}}} \right) $
Find the factors of the term in the numerator and the denominator.
The resulting value $ = 2 \times 6 \times 10 \times 100 \times \left( {\dfrac{{75}}{{100}}} \right) \times \left( {\dfrac{{25 \times 5}}{{10 \times 10}}} \right) $
Common multiple from the numerator and the denominator cancels each other.
The resulting value $ = 6 \times 75 \times 25 $
Simplify the above expression finding the product of the terms.
The resulting value $ = 11250 $
This is the required solution.
So, the correct answer is “11250”.

Note: Be good in multiples and find the prime factors. Common factors from the numerator and the denominator cancels each other. Always try to find out the common factors from the numerator and the denominator. Understand the given data and frame the equation correctly and check it twice since the solution depends on it only.