Question

The ratio of ram and shyam 5 years ago was 2:5 and the ration of this age after 5 years will be 3:4.Find the sum of their present age

Answer 1

Given:

The ratio of ram and shyam 5 years ago was 2:5 and the ratio of this age after 5 years will be 3:4.

To find:

The sum of their present age

Solution:

Let,

"R" → represents the present age of Ram

"S" → represents the present age of Shyam

Age 5 years ago:

Ram's age = R - 5

Shyam's age = S - 5

As given in the question, we get

$\frac{R - 5}{S- 5 } = \frac{2}{5}$

$\implies 5(R - 5) = 2(S- 5)$

$\implies 5R - 25 = 2S- 10$

$\implies 5R - 2S = 15$ . . . . Equation 1

Age after 5 years:

Ram's age = R + 5

Shyam's age = S + 5

As given in the question, we get

$\frac{R + 5}{S+ 5 } = \frac{3}{4}$

$\implies 4(R + 5) = 3(S+ 5)$

$\implies 4R + 20 = 3S+ 15$

$\implies 4R - 3S = -5$ . . . . Equation 2

On multiplying equation 1 by 3 and equation 2 by 2, we get

$15R - 6S = 45$ . . . . Equation 3

$8R - 6S = -10$ . . . . Equation 4

On subtracting equation 3 and 4, we get

15R - 6S = 45

8R - 6S = -10

-     +        +

----------------------

7R = 35

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∴ R = $\frac{35}{7}$ = 5 years

On substituting the value of R in equation 1, we get

(5 × 5) - 2S = 15

⇒ 25 - 2S = 15

⇒ 2S = 10

⇒ S = 5 years

Therefore,

The sum of the present age of Ram and Shyam = 5 + 5 = 10 years

Thus, the sum of their present age is → 10 years.

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Also View:

The present age of Ram and Shyam are in the ratio of 4:5 after eight-year. The ratio of their ages will be 5:6. Find their present ages?

brainly.in/question/7807726

The present ages of Ram and Shyam are in the ratio 5 : 6. Five years ago, the ratio was 4:5. Find their present ages.

brainly.in/question/10163043

Answer 2

SOLUTION

GIVEN

The ratio of Ram and Shyam 5 years ago was 2 : 5 and the ration of this age after 5 years will be 3 : 4.

TO DETERMINE

The sum of their present age

CONCEPT TO BE IMPLEMENTED

Ratio :

Ratio means comparing of two quantities

The ratio of a number a to another number b ( where b # 0) is a fraction a/b and it is written a : b , the first term a is called antecedent and the second term is called consequent

EVALUATION

Here it is given that the ratio of Ram and Shyam 5 years ago was 2 : 5

Let 5 years ago -

Age of Ram was = 2x years

Age of Shyam was = 5x years

So

Present age of Ram = 2x + 5 years

Present age of Shyam = 5x + 5 years

So after 5 years -

Age of Ram will be

= 2x + 5 + 5 years

= 2x + 10 years

Age of Shyam will be

= 5x + 5 + 5 years

= 5x + 10 years

So by the given condition

$\displaystyle \sf{ \frac{2x + 10}{5x + 10} = \frac{3}{4} }$

$\displaystyle \sf{ \implies \: 15x + 30 = 8x + 40}$

$\displaystyle \sf{ \implies \: 7x = 10 }$

So the required sum of present ages of Ram and Shyam

= ( 2x + 5 + 5x + 5 ) years

= ( 7x + 10 ) years

= 10 + 10 years

= 20 years

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