Question

Radhe is twice as old as karan 10 years ago radhe was three times as old as karan find radhe's present age
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Answer 1

Given info:

• Radhe is twice as old as Karan.
• 10 years ago, radhe was three times as old as Karan.

Let's say,

• The Present age of Karan is M years.
• Then, the present age of Radhe will be 2M years.

• As⠀P e r⠀Q u e s t i O n :

• 10 years ago, radhe was three times as old as Karan. Therefore:

⌑ 10 years ago, their ages:

• Karan's age = (M – 10) years
• Radhe's age = (2M – 10) years

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

✇ Now, we've been given that before 10 years, the age of Radhe was 3 times of the age of Karan$.$ Making a Linear equation:

★⠀Radhe's age = 3(Karan's age) ★

↠⠀(2M – 10) = 3(M – 10)

↠⠀2M – 10 = 3M – 30

↠⠀2M – 3M = – 30 + 10

↠⠀– M = – 20

↠⠀M = 20

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

Therefore,

• The Present age of Karan, M = 20 years
• The Present age of Radhe, 2M = 2(20) = 40 years

⠀

❝ Hence, Present age of Radhe is 40 years. ❞

Answer 2

G I V E N :

Radhe is twice as old as karan. 10 years ago radhe was three times as old as karan find radhe's present age ?

S O L U I O N :

Let us assume ⤵

Karan's age be a

Now, according to the question -

Radha is twice as old as Karan

Hence, Radha's age be 2a

10 years ago ⤵

Radha's age was 2a - 10

Karan's age was a - 10

Ratio of their ages ⤵

Radha was three times as old as Karan

Hence,

Radha : Karan = 3 : 1

So, the equation is :

$\twoheadrightarrow \frak{ \frac{2a - 10}{a - 10} = \frac{3}{1} }$

Cross multiplying we get

$\twoheadrightarrow \frak{1(2a - 10) = 3(a - 10)}$

$\twoheadrightarrow \frak{2a - 10 = 3a - 30}$

Transposing them we have

$\twoheadrightarrow \frak{2a - 3a = - 30 + 10}$

$\twoheadrightarrow \frak{ - a = - 20}$

$\twoheadrightarrow \frak{ \cancel - a = \cancel - 20}$

$\star \: \red{ \underline{ \purple{ \boxed{ \frak{a = 20}}}}}$

____________________________

Finding Ages ⤵

Radha's present age = 2a = 2 × 20 = 40 years

Karan's present age = a = 20 years

☞ Radha's age is 40 yrs and Karan's age is 20 yrs