Question

Ravi's salary is 150% of Amit's salary. Amit's salary is 80% of Ram's salary. What is the ratio of Ram's salary to Ravi's salary?
A) $\dfrac{5}{7}$
B) $\dfrac{5}{9}$
C) $\dfrac{5}{6}$
D) $\dfrac{1}{6}$

Answer 1

Hint: First, assume the salary of Ram. Then, find the salary of Amit in terms of that. After that calculate the salary of Ravi in terms of the salary calculated by Amit. Then, calculate the ratio of the salary of Ram to the salary of Ravi.

Complete step-by-step answer:
Given:- Ravi's salary is 150% of Amit's salary and Amit's salary is 80% of Ram's salary.
The ratio is termed as the quantity of one thing is compared to another thing.
Let the salary of Ram be x.
Since Amit's salary is 80% of Ram's salary. Then, the salary of Amit is 80% of x,
$\dfrac{{80}}{{100}} \times x$
Cancel out the common factors from numerator and denominator,
$\dfrac{4}{5}x$
So, the salary of Amit is $\dfrac{4}{5}x$.
Now, Ravi's salary is 150% of Amit's salary. Then, the salary of Amit is 150% of $\dfrac{4}{5}x$,
$\dfrac{{150}}{{100}} \times \dfrac{4}{5}x$
Cancel out the common factors from numerator and denominator,
$\dfrac{6}{5}x$
Now, calculate the ratio of the salary of Ram to the salary of Ravi.
$Ratio = \dfrac{a}{b}$
Put $a = x$ and $b = \dfrac{6}{5}x$.
$Ratio = \dfrac{x}{{\dfrac{6}{5}x}}$
Cancel out x from numerator and denominator and shift 5 to the numerator,
$Ratio = \dfrac{5}{6}$
Thus, the ratio of the salary of Ram to the salary of Ravi is $\dfrac{5}{6}$ or $5:6$.

Hence, option (C) is correct.

Note: The students must assume the salary of Ram to solve the problem in easy and simple calculations. If he/she assumes the salary of Amit, it will make the lengthy calculation to calculate the salary of Ram or if he/she assumes the salary of Ravi, the whole solution will be lengthy and there will be a huge chance to do calculation error and get the wrong ratio.