Question

If the numerator of a fraction is increased by 200% and the denominator is increased by 350%, the resultant fraction is $\dfrac{5}{12}$, what was the original fraction?
(a) $\dfrac{5}{9}$
(b) $\dfrac{5}{8}$
(c) $\dfrac{7}{12}$
(d) $\dfrac{11}{12}$

Answer 1

Hint: In this problem, we will use the definition of percentage to find the original fraction. A fraction is represented as $\dfrac{p}{q}$, where p and q are integers. We will assume the original fraction as a fraction as a variable and then we will proceed.

Complete step-by-step answer:
From the definition of percentage we know that x% of any number y is = $\dfrac{x}{100}\times y..........\left( 1 \right)$
By the word percent it means that out of 100 and thus at the above formula.
Let us consider that the original fraction is = $\dfrac{a}{b}$
So, ‘a’ is the numerator and ‘b’ is the denominator.
It is given that a in increased by 200%. So, using equation (1) a will become:
$a+\dfrac{200}{100}\times a=a+2a=3a$
It is also given that b is increased by 350%. So, again using the equation (1), b becomes:
$b+\dfrac{350}{100}\times b=b+3.54.5b$
So, the new fraction obtained after applying the given conditions is equal to = $\dfrac{3a}{4.5b}$
 Since, the given value of new fraction in the question is = $\dfrac{5}{12}$
So, we can equate these two new fractions as they must be equal to each other.
Therefore, $\dfrac{3a}{4.5b}=\dfrac{5}{12}$
Or, $\dfrac{a}{b}=\dfrac{5}{12}\times \dfrac{4.5}{3}$
We can divide and multiply by 10 to the right side to remove the decimal. So, we get:
$\dfrac{a}{b}=\dfrac{5}{12}\times \dfrac{45}{30}$
On further simplification we get:
$\dfrac{a}{b}=\dfrac{5}{8}$
So, the value of the original fraction is $\dfrac{5}{8}$.
Hence, option (b) is the correct answer.

Note: Students should remember that the meaning of percentage is something out of 100. So, this is why it is necessary to divide the given value of percentage by 100 and do the calculation part correctly to avoid mistakes.