Question

the ratio of the ages of a man and his wife is 6 : 5. after 16 years, the ratio becames 10 : 9. find the husband's age when the wife was born

Answer 1

let the husband age be 6x
let wife age be 5x
after 16 years
their ages are
husband =10x
wife=9x
ATQ
5x+16+6x+16=10x+9x
11x+32=19x
11x-19x=-32
-8x=-32.
x=-32/-8
x=4
so, husband present age =6x=6*4=24
wife present age=5x=5*4=20
so wife was born 20years ago

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Answer 2

↑ Here is your answer ↓
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Let the age of man be 'x' and wife be 'y'

$x/y = 6/5$

$5x = 6y$

$5x - 6y = 0---(1)$

Second equation,

$(x+16)/(y+16) = 10/9$

$9x + 144 = 10y + 160$

$9x + 144 - 10y - 160 = 0$

$9x - 10y - 16 = 0$

$9x - 10y = 16---(2)$

Subtract (1) from (2),

$4y = 80$

$y = 80/4$

$y = 20$

Substiture 'y = 20' in any equation,

$x = 24$

Husband's age when his wife was born!

$= 24 - 20$

$= 4$