Question

five
years ago,
Nuri was 2/5
time as old as fonu.
Six
years
lates
Nuri will be 5/7
Times
as sones How old are nuri & Sonu

Answer 1

Question:

Five years ago, Nuri was 2/5 times as old as Sonu. Six years later Nuri will be 5/7 times as Sonu. How old are Nuri & Sonu?

Answer:-

Let present age of Sonu be x years.

Given:

Nuri was 2/5 times as old as Sonu 5 years ago.

Sonu's age before 5 years = (x - 5) years.

Hence,

⟶ Nuri's age - 5 = 2/5 * (x - 5)

⟶ Nuri's age = [ (2x - 10)/5 ] + 5

⟶ Nuri's age = [ 2x - 10 + 25 ] / 5

⟶ Nuri's age = (2x + 15)/5 -- equation (1)

Also,

After 6 six years , Nuri's age will be 5/7th of sonu's age.

⟶ Nuri's age + 6 = 5/7 * (x + 6)

⟶ (2x + 15)/5 + 6 = (5x + 30)/7

⟶ (2x + 15 + 30) / 5 = (5x + 30)/7

⟶ (2x + 45) * 7 = 5 * (5x + 30)

⟶ 14x + 315 = 25x + 150

⟶ 315 - 150 = 25x - 14x

⟶ 165 = 11x

⟶ 15 = x

⟶ Sonu's age = 15 years

Substitute x value in equation (1).

⟶ Nuri's age = [ 2(15) + 15 ] / 5

⟶ Nuri's age = ( 30 + 15) / 5

⟶ Nuri's age = 45/5

⟶ Nuri's age = 9 years

Therefore,Sonu's age is 15 years and that of Nuri is 9 years.

Answer 2

$\mathcal{\green{\underline{\underline{\red{QUESTION:-}}}}}$

✨ Five years ago, Nuri was 2/5 times as old as Sonu . Six years later, Nuri will be 5/7 times as old as Sonu . How old are Nuri & Sonu ?

$\mathcal{\green{\underline{\underline{\red{ANSWER:-}}}}}$

$\bf{\gray{\underbrace{\blue{GIVEN:-}}}}$

• Five years ago, Nuri was 2/5 times as old as Sonu .

• Six years later, Nuri will be 5/7 times as old as Sonu .

$\bf{\gray{\underbrace{\blue{TO\:FIND:-}}}}$

1. The present age of Nuri .
2. The present age of Sonu .

$\bf{\gray{\underbrace{\blue{SOLUTION:-}}}}$

Let,

• Present age of Sonu be "X years" .

• Present age of Nuri be "Y years" .

Before 5 years :-

• Sonu's age = (X - 5) years

• Nuri's age = (Y - 5) years

According to the question,

CASE - 1 :-

⟹ Y - 5 = 2/5 × (X - 5)

⟹ Y = 2X/5 - 2 + 5

⟹ Y = 2X/5 + 3 ----(1)

After 6 years :-

• Sonu's age = (X + 6) years

• Nuri's age = (Y + 6) years

CASE - 2 :-

⟹ Y + 6 = 5/7 (X + 6)

⟹ Y = 5X/7 + 30/7 - 6

⟹ Y = 5X/7 - 12/7 ----(2)

Now, putting the value of Y from Equation (1), in the equation (2)

➳ 2X/5 + 3 = 5X/7 - 12/7

➳ 5X/7 - 2X/5 = 12/7 + 3

➳ (25X - 14X)/35 = 33/7

➳ 11X = 33/7 × 35

➳ X = (33 × 5)/11

➳ X = 3 × 5

➳ X = 15 years

Putting the value of X in the equation (1), we get

➳ Y = (2 × 15)/5 + 3

➳ Y = 30/5 + 3

➳ Y = 6 + 3

➳ Y = 9 years

__________________________

$\red\therefore$ [1] The present age of Nuri is "15years"

$\red\therefore$ [2] The present age of Sonu is "9years"