Question

present age of Anu and Raj are in the ratio 4:5 8 years from now the ratio of their ages will be 5:6
find their present age ​

Answer 1

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Given:-

Present ages of Anu and Raj are in the ratio = 4:5

Let present age of Anu = 4x Years

& present age of Raj = 5x years

After 8 years from now,

• Anu's age = (4x+8) years
• Raj's age = (5x + 8) years

Ratio of ages after 8 years is 5:6

$\sf \: \frac{Anu's \: age \: after \: 8 \: years}{Raj's \: age \: after \: 8 \: years} = \frac{5}{6}$

$\sf \frac{4x + 8}{5x + 8} = \frac{5}{6}$

★ By cross-multiplication

$\sf \: 6 (4x+8)=5 (5x + 8)$

$\sf \longrightarrow \: (6 \times 4)x+ (6 \times 8) = (5 \times 5)x+ (5 \times 8)$

$\sf \longrightarrow \: 24x +48= 25x + 40$

$\sf \longrightarrow \: 48 - 40 = 25x - 24x$

$\sf \longrightarrow 8 = x$

$\sf \longrightarrow x = 8$

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$\sf \therefore \: Present \: age \: of \: Anu = 4x = 4 \times 8 = 32 years$

$\sf \:Present \: age \: of \: Raj = 5x = 5 \times 8 = 40 \: Years$

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Answer 2

Answer:

present age of Anu is 32 and raj is 40

Step-by-step explanation:

Let ages if them be 4x and 5x

according to question:

4x+8+5x+8 = 5x+6x

4x+5x+8+8 = 11x

9x+16x = 11x

16x = 11x-9x

16x = 2x

x = 16/2

x = 8

present age of Anu = 4x = 4×8 = 32

present age of Raj = 5x = 5×8 = 40

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