Question

8.
The present age of A and B are in the ratio
of 8 : 7.27 years ago their age was in the
ratio 5:4. Find the age of elder one​

Answer 1

Question:

The present age of A and B are in the ratio

of 8 : 7 . 27 years ago their age was in the

ratio 5:4 . Find the age of the elder one.

Answer:

72 years

Solution:

It is given that;

The present age of A and B are in the ratio

of 8 : 7.

Thus,

Let's assume that:

A's present age = 8x years

B's present age = 7x years

Also,

27 years ago ;

A's age = (8x - 27) years

B's age = (7x - 27) years

Now,

According to the question;

27 years ago their age was in the ratio 5:4 .

Thus;

=> (8x - 27):(7x - 27) = 5:4

=> (8x - 27)/(7x - 27) = 5/4

=> 4•(8x - 27) = 5•(7x - 27)

=> 32x - 4•27 = 35x - 5•27

=> 5•27 - 4•27 = 35x - 32x

=> 27•(5 - 4) = 3x

=> 27•1 = 3x

=> 3x = 27

=> x = 27/3

=> x = 9

Thus,

A's present age = 8x years

= 8•9 years

= 72 years

B's present age = 7x years

= 7•9 years

= 63 years

Clearly, here A is elder than B .

Hence,

The present age of elder one is 72 years .

Answer 2

Given :---

• Present age ratio = 8:7
• 27 years ago ratio = 5:4
• Find elder one age ..

Solution (1)

→ Let present age of A = 8x

→ Let Present age of B = 7x

Now,

→ Before 27 years A was = (8x-27)

→ Before 27 years B was = (7x-27)

According to Question Their Ratio was 5:4:,

so,

→ (8x-27):(7x-27) = 5:4

→ 4(8x-27) = 5(7x-27)

→ 32x -27*4 = 35x - 27*5

→ 35x-32x = 27(5-4)

→ 3x = 27

→ x = 9

So, A present age = 8x = 8*9 = 72 years.

and , B present age = 7x = 7*9 = 63 years .

Hence, Elder one is A and he is 72 years old ..

______________________________

Solution (2)

Shortcut Trick to Solve Question :

⋆ Present Age⠀⠀➞27 Yrs.⠀⋆ Before Age

Sona : Sonali⠀⠀⠀⠀⠀⠀⠀⠀⠀Sona : Sonali

⠀⠀8 : 7⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀5 : 4

◗ Difference of both Ratios is

(8 - 5) = and, (7 - 4) = 3,

so,

Divide Year Gap By that Number.

↦ Year Gap / Difference of Age

↦ 27 Years / 3

↦ 9

Now, Just Multiply the Outcome (9 in this Case) with any of the Ratio of find Age.

Here we have to Find Present Age :

◗ A = (8 × 9) = 72 Years

◗ B = (7 × 9) = 63 Years

∴ Therefore, Present Age of Elder one that is A is 72 Years ...