Question

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Answer 1

Given :-

The ratio of Rakesh and Reeta's age =≥ 4:3 before 10 years

Sum of their present ages is 55

To find :-

Their present ages

What is ratio?

Ratio is the relation between any two quantities in their lowest forms.

Let's take an example.

Ratio of 25kg to 10kg is 25:10

As we know that ratio is expressed in the lowest terms, the ratio between the two weights will be 5:2

Hence, If the ratio of Rakesh and Reeta is 4:3 then their actual ages must be a multiple of a common number/factor.

Let that common number/factor be x.

The ages will be 4x and 3x before 10 years.

According to the question,

Their present ages = 4x + 10 and 3x + 10

By forming the Linear Equation,

4x + 10 + 3x + 10 = 55

Adding the like terms,

7x + 20 = 55

Transposing 10 to the RHS (Right Hand Side),

7x = 55 - 20

7x = 35

By transposing 7 to the RHS (Right Hand Side),

$x = \dfrac{45}{7}$

$x = 5$

Therefore their ages before 10 years :-

Rakesh :- 4x = 4(5) = 20 years

Reeta :- 3x = 3(5) = 15 years

Present ages :-

Rakesh :- 20 + 10 = 30 years

Reeta :- 15 + 10 = 25 years

Verification :-

Let us substitute 4x + 10 and 3x + 10 as 30 and 25 respectively

30 + 25 = 55

LHS = RHS

Hence verified