Question

$\bf\huge\tt\bigstar\pink{plezz \: solve}\bigstar$
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Answer 1

Step-by-step explanation:

Question:-

Ten years ago the ratio of the ages of Ramesh and Suresh was 1: 5 . Ten years hence the ratio of their ages will be 3 : 5 then,

Find the present age of Ramesh.

How old was Suresh ten years ago?

Solution:-

Let the present age of Ramesh be x

And the present age of Suresh be y

Ten years ago:-

Age of Ramesh = x - 10

Age of Suresh = y - 10

The ratio of the ages of their was 1:5

$\sf\implies \dfrac{x - 10}{y - 10} = \dfrac{1}{5}$

$\sf\implies 5(x - 10) = y - 10$

$\sf\implies 5x - 50 = y - 10$

$\sf\implies 5x - y = 40......(i)$

Ten years later:-

Age of Ramesh = x + 10

Age of Suresh = y + 10

The ratio of their ages will be 3 : 5

$\sf\implies \dfrac{x + 10}{y + 10} = \dfrac{3}{5}$

$\sf\implies 5(x + 10) = 3(y + 10)$

$\sf\implies 5x + 50 = 3y + 30$

$\sf\implies 5x - 3y = -20......(ii)$

Equation (i) - (ii):-

$\sf \implies 5x - y - (5x - 3y) = 40 - (-20)$

$\sf \implies 5x - y - 5x + 3y = 40 + 20$

$\sf \implies 2y = 60$

$\sf \implies y = 30$

Substitute y = 30 in equation (i):-

$\sf\implies 5x - 30 = 40$

$\sf\implies 5x = 70$

$\sf\implies x = 14$

$\underline{\boxed{\therefore \textsf{\textbf{ Present \: age \: of \: Ramesh = 14 \: years}}}}$

$\leadsto\underline{\sf 58 : Option \: (1)}$

Age of Suresh 10 years ago:-

= y - 10

= 30 - 10 = 20 years

$\leadsto \underline{\sf 59 : Option \: (2)}$

Answer 2

$\huge\underline\mathfrak\color{pink}Given:-$

Ten years ago Ramesh Age : Suresh Age

1 : 5

10 years later, 3 : 5

Let the present ratio x : y

Ten years ago ratio x - 10 : y - 10

Ten years later ratio x + 10 : y + 10

Compare ratio of ten years ago

$\frac{x - 10}{y - 10} = \frac{1}{5}$

5x - 50 = y - 10

5x - y = 40 ------> Eq. 1

Compare ratio of ten years later

$\frac{x + 10}{y + 10} = \frac{3}{5}$

5x + 50 = 3y + 30

5x - 3y = - 20 --------> Eq. 2

Solve equation 1 & 2, substitute 2 from 1

(5x - y) - (5x - 3y) = 40 - ( - 20)

2y = 60

$\fbox\pink{y = 30}$

5x = 40 + 30

$x = \frac{70}{5} = 14$

$\fbox\pink{x = 14}$

a) Present age of Ramesh = x

= 14 years

$\fbox\blue{option \: (1) \: is \: correct \: }$

b) Suresh age ten years ago = y - 10

= 30 - 10

= 20 years

$\fbox\red{option \: (2) \: is \: correct}$