Question

The ratio between Ram’s age and Rahim’s age is $ 10:11 $ . What is the age of Rahim in percentage of Ram’s age?
A. $ 109\dfrac{1}{11} $ %
B. 110%
C. $ 111\dfrac{1}{9} $ %
D. 111%

Answer 1

Hint: We first assume the ratio constant to find the present ages of Ram and Rahim. Now we need to find the percentage of Rahim’s age with respect to Ram’s age. We use the formula of $ \dfrac{\text{Rahim }\!\!'\!\!\text{ s age}}{\text{Ram }\!\!'\!\!\text{ s age}}\times 100 $ to find the percentage. We place the values of ages to find the percentage.

Complete step by step answer:
The ratio between Ram’s age and Rahim’s age is $ 10:11 $.
We assume the ratio constant to find their present ages. Let the constant ratio be x.
So, their present ages are 10x and 11x respectively.
We need to find the age of Rahim in the percentage of Ram’s age. This means we need the respective age of Rahim.
We need to find the percentage of 11x with respect to 10x.
The percentage formula is $ \dfrac{\text{Rahim }\!\!'\!\!\text{ s age}}{\text{Ram }\!\!'\!\!\text{ s age}}\times 100 $ .
We place the values to find the percentage value.
The percentage is $ \dfrac{\text{Rahim }\!\!'\!\!\text{ s age}}{\text{Ram }\!\!'\!\!\text{ s age}}\times 100=\dfrac{11x}{10x}\times 100=110 $ .
Therefore, Rahim’s age is 110% of Ram’s age.
The correct option is B.

Note:
The use of constant is obsolete when we are finding respective percentages. All the relation between two same units is based on the ratio. The ratio multiplied by 100 gives us the percentage. We could have solved the problem without taking the constant ratio where we get $ \dfrac{11}{10}\times 100=110 $.