Question

A number when decreased by 16% becomes 798; find the number?

Answer 1

Hint: We start solving the problem by assigning the variable for the value of the number. We then decrease the variable by 16% using the fact that a% of b is $\dfrac{a}{100}\times b$. We then equate it to the given number 798 and make the necessary calculations to get the value of the original number.

Complete step-by-step solution
According to the problem, we need to find the number which gives 768 to decrease it by 16%.
Let us assume the number is ‘x’.
We need to decrease this number by 16%. So, the new number will be 16% less than the original number which is $\left( 100-16 \right)\%=84\%$ of ‘x’.
We know that a% of b is defined as $\dfrac{a}{100}\times b$.
So, we get 84% of x as $\dfrac{84}{100}\times x=0.84x$.
According to the problem, it is mentioned that the number of 0.84x is equal to 798.
So, we have $0.84x=798$.
$\Rightarrow x=\dfrac{798}{0.84}$.
$\Rightarrow x=950$.
So, we have found the value of the required number as 950.

Note: Whenever we get this type of problem, we try to start solving it by assigning the variable for the unknowns to avoid confusion and calculation mistakes. We should confuse a% of b with $a\times b$ instead of $\dfrac{a}{100}\times b$. We can also find the percentage at which the number 798 has to be increased to get 950 in a similar process. Similarly, we can expect problems involving the addition and subtraction of variables.