Question

16. The ratio of ages of two persons is 7: 11. Seven years hence, the ratio of their ages will be 2:3
Find their present ages.​

Answer 1

Answer:-

Let's take a common factor between the ratios

Let's take a common factor between the ratiosLet the common factor be $x$

So, the present ages of the two persons are $7x$ and $11x$ respectively.

After 7 years there ages will be $\frac{7x + 7}{11x + 7}$

Therefore according to the question the equation formed is

$\frac{7x + 7}{11x + 7} = \frac{2}{3}$

$= > 3(7x + 7) = 2(11x + 7)$

$= > 21x + 21 = 22x + 14$

$= > 21x - 22x = 14 - 21$

$= > - x = - 7$

$= > - x \times ( - 1) = - 7 \times ( - 1)$

$= > x = 7$

∴ Present age of one person = 7x

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ = 7 × 7

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ = 49

Present age of another person = 11x

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ = 11 × 7

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ = 77

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Answer 2

Given :

• The ratio of ages of two persons is 7 : 11
• Seven years hence, the ratio of their ages will be 2 : 3

To Find :

• Their present ages

Solution :

Let, the common factor be 'x'

Given that,

• The ratio of ages of two persons is 7 : 11

So, the present ages of the two persons are '7x' and '11x' respectively$.$

☆ After 7 years,

Their ages will be '7x + 5' and '11x + 5'

A.T.Q :

⇒ (7x + 5)/(11x + 5) = 2/3

⇒ 3(7x + 5) = 2(11x + 5)

⇒ 21x + 15 = 22x + 10

⇒ 21x - 22x = 10 - 15

⇒ - x = - 5

⇒ x = 5

∴ Present age of 1st person = 7x

$\: \: \: \: \: \: \:\:\: \: \: \: \: \: \: \:\:\: \: \:\: \: \:\: \: \: \: \: \: \:\:\: \: \: \: \: \: \:\:\: \: \: \:\:\: \: \: \: \: \: \: \:\:\: \: \:$= 7 × 5

$\: \: \: \: \: \: \: \: \:\:\: \:\: \: \:\: \:\: \: \: \: \:\:\: \: \: \:\: \: \: \: \:\:\: \: \: \: \: \: \: \: \:\:\: \: \: \: \: \: \: \:\:\: \: \: \:$= 35 year

∴ Present age of 2nd person = 11x

$\: \: \: \: \: \:\: \: \: \: \:\: \: \: \: \: \: \:\:\: \: \: \: \: \: \: \:\:\: \: \: \: \: \: \:\:\: \: \:\: \: \:\: \: \: \:\:\: \: \: \:\:\: \: \: \:$= 11 × 5

$\: \: \: \: \: \: \:\:\: \: \:\: \: \: \: \: \: \:\: \: \: \: \: \: \:\:\: \: \:\:\: \: \: \: \: \:\:\: \: \: \: \:\:\: \: \: \: \: \: \: \:\:\: \: \: \:$= 55 year

Verification :

We have,

⇒ (7x + 5)/(11x + 5) = 2/3

Substituting the value of x,

⇒ {7(5) + 5}/{11(5) + 5} = 2/3

⇒ (35 + 5)/(55 +5) = 2/3

⇒ (40)/60 = 2/3

⇒ 2/3 = 2/3

HENCE VERIFIED