Question

The present ages of A and B are in the ratio of 5:2. Two years ago, the ratio of their ages was 4:1. Find their present ages.

Answer 1

Answer:

et the age of A and B are 4x and 5x

According  to question,  

ten years ago ,  

5x−10

4x−10 = 4 3 (4x−10)4=(5x−10)3

16x−40=15x−30

x=10

So their present ages are 4(10)=40 , 5(10)=50.

Answer 2

Given :

The present ages of A and B are in the ratio of 5:2. Two years ago, the ratio of their ages was 4:1.

To Find :

Their present ages.

Solution :

Analysis :

Here we have to form equations. Solving those equations we can find the value of x and from that x we can get the present ages.

Explanation :

Let us assume that the age of A is "5x" years.

Age of B is "2x" years.

Two years ago,

• A = (5x - 2) years
• B = (2x - 2) years

Two years ago their ratio was 4 : 1.

☯ According to the question,

$\implies\sf\dfrac{5x-2}{2x-2}=\dfrac{4}{1}$

Cross multiplying,

⇒ 5x - 2 = 4(2x - 2)

Expanding the brackets,

⇒ 5x - 2 = 8x - 8

Transposing 5x to RHS and -8 to LHS,

⇒ -2 + 8 = 8x - 5x

⇒ 6 = 3x

⇒ 6/3 = x

⇒ 2 = x

∴ x = 2.

Their present ages :

• A = 5x = 5 × 2 = 10 years
• B = 2x = 2 × 2 = 4 years.

Present age of A is 10 years.

Present age of B is 4 years.

Verification :

• Putting x = 2,

$\implies\sf\dfrac{5(2)-2}{2(2)-2}=\dfrac{4}{1}$

$\implies\sf\dfrac{10-2}{4-2}=\dfrac{4}{1}$

⇒ 8/2 = 4/1

Cancelling LHS with 2,

⇒ 4/1 = 4/1

∴ LHS = RHS.

• Hence verified.