Question

The present ages of Amit and Sumit are in the ratio 11:8. After eight years, the ratio of their ages will be 5: 4. Find their present ages.​

Answer 1

Let,

• Amit's age = 11x
• Sumit's age = 8x

8 years hence,

• Age of Amit = 11x + 8
• Age of Sumit = 8x +8

Therefore, their ratio of ages will be:

(11x + 8) : (8x + 8)

A/Q,

⟹ (11x + 8) : (8x + 8) = 5:4

⟹ $\sf\dfrac{(11x + 8)}{(8x+8)} = \sf\dfrac{5}{4}$

Cross Multiplying

⟹ (11x + 8)4 = (8x + 8)5

We can write it as

⟹ 4(11x + 8) = 5(8x + 8)

⟹ 44x + 32 = 40x + 40

⟹ 44x - 40x = 40 - 32

⟹ 4x = 8

Cancelling

⟹ x = $\sf\cancel\dfrac{8}{4}$

⟹ x = 2.

We have assumed the present ages of Amit as 11x and Sonu as 8x. So, their present ages are:

• Amit's age = 11x = 11×2 = 22years
• Sonu's age = 8x = 8×2 = 16years.

Hence, their present ages are 22 and 16 years respectively.

Answer 2

Given :

• Ratio of present ages of Amit And Sumit = 11:8
• Ratio of their ages after 8 years = 5:4
• Their ages = ???

To Find :

We have to find out the present ages of Amit and Sumit

Let's Assume :

Let's Assume that the ages of Amit and Sumit are :

• Age of Amit = 11x
• Age of Sumit = 8x

So, after 8 years , their ages will be :

• Age of Amit (After 8 years) = 11x+8
• Age of Sumit (After 8 years) = 8x+8

To Be done :

We will first Assume the present ages of Amit and Sumit and Also their ages after 8 years (See the 'Let's Assume' part)

Now, taking that assumed ages, we will compare it with the given Ratio and calculate the value of unknown .

Solution :

Age of Amit after 8 years = 11x+8

Age of Sumit after 8 years = 8x+8

$\large \tt{ \implies \: \frac{11x + 8}{8x + 8} = \frac{5}{4} }$

$\large \tt{ \implies \: 4(11x + 8) = 5(8x + 8)}$

$\large\tt{ \implies \: 44x + 32 = 40x + 40}$

$\large\implies \tt{44x - 40x = 40 - 32}$

$\large{ \tt{ \implies \: 4x = 8}}$

$\large \red{ \underline{ \boxed{ \tt{ \therefore \: x = 2}}}}$

Hence, X = 2

So, the ages of Amit and Sumit are :

• Age of Amit = 11x = 11×2 = 22 years
• Age of Sumit = 8x = 8×2 = 16 years