Question

The present age of lavanya's mother is 3 times that of sumathi. After 5 years the sum of their ages will be 70 years. Find their present ages? ​

Answer 1

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$let \: age \: of \: the \: son \: be \: x \\ so \: age \: of \: mother \: = 3x \: = y$

$\\ after \: 5 \: years \: their \: sum \: of \: ages \: = 70$

$so \: (x + 5) + (y + 5) = 70 \\ x + 5 + 3 + 5 = 70 \\ 4x + 10 = 70 \\ 4x = 60 \\ x = 15$

$\\ so \: present \: age \: of \: son = \: 15 \: years \\ present \: age \: of \: mother = 3 \times 15 = 45 \: yrs$

$so \: after \: 10 \: yrs \: her \: age \: is \: = \\ 45 + 10 = 55 \: yrs$