Sum of ages of father and son at present is 33,years. Two years ago product of their ages was 28 ,ye

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The sum of the ages of father and son at present is $33\,years.$ Two years ago the product of their ages was $28 \,years.$ What is the age of the father and the son? (in $years$)

A

$26,7$

B

$30,3$

C

$29,4$

D

$32,1$

Solution

$F + S =33 \Rightarrow F =33- S$

$(F-2) \times(S-2)=28$

$(33- S -2) \times( S -2)=28$

$(31-S)(S-2)=28$

$31 S -62- S ^{2}+25=28$

$\Rightarrow-S^{ 2}+33 S-62=28$

$\Rightarrow-S ^{2}+33 S-90=0$

$\Rightarrow S^{ 2}-33 S +90=0$

$(S-33)(S-3)=0$

$S=3$

$\therefore F=33-3=30$

Standard 13

Quantitative Aptitude

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