Question

The ages of Raju and Ravi are in the ratio 3:4 .Four years from now the ratio of their ages will be 4:5 . Find their present ages. In Steps

Answer 1

☀️  Given that, the ages of Raju and Ravi are in the ratio 3:4  and four years from now the ratio of their ages will be 4:5.

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━

❍ Let's say that,

• Present age of Raju be ' 3x ' years
• Present age of Ravi be ' 4x ' years

A/Q,

⤳  ( 3x + 4 )/( 4x + 4 ) = 4/5

⤳  5( 3x + 4 ) = 4( 4x + 4)

⤳  15x + 20 = 16x + 16

⤳  16x - 15x = 20 - 16

⤳  x = 4

T H E R E F O R E,

• Present age of Raju = 3x

→ 3 × 4

→ 12 years

• Present age of Ravi = 4x

→ 4 × 4

→ 16 years

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━

• Henceforth, present age of Raju is 12 years and Ravi is 16 years.

Answer 2

$let \: age \: of \: raju = 3x$

$age \: of \: ravi = 4x$

$after \: four \: years$

$age \: of \: raju = 4y = 3x + 4$

$age \: of \: ravi = 5y = 4x + 4$

$\frac{3x + 4}{4x + 4} = \frac{4 \cancel y}{5 \cancel y}$

$\frac{3x + 4}{4x + 4} = \frac{4}{5}$

$5(3x + 4) = 4(4x + 4)$

$15x + 20 = 16x + 16$

$15x - 16x = 16 - 20$

$- x = - 4$

$x = 4$

$age \: of \: raju = 3 \times 4 = 12$

$age \: of \: ravi = 4 \times 4 = 16$