Question

three times as old as her son 5 years hence the sum of their ages will be 70 years find their present ages​

Answer 1

✬ Son's Age = 15 Years ✬

✬ Mother's Age = 45 Years ✬

Step-by-step explanation:

Correct Question:

• Mother is three time as old as her son 5 years hence the sum of their ages will be 70 years find their present ages.

Given:

• Mother is 3 times as old as her son.
• After 5 year sum of their ages will be 70 years.

To Find:

• Present ages of both ?

Solution: Let the present age of son be x years. Therefore ,

➮ Present age of mother = 3 times of x

➮ 3x years

[ After 5 years their ages will be ]

• Son's age = (x + 5) years

• Mother's age = (3x + 5) years

A/q

$\implies{\rm }$ ( Mother's + Son's )age = 70

$\implies{\rm }$ 3x + 5 + x + 5 = 70

$\implies{\rm }$ 4x + 10 = 70

$\implies{\rm }$ 4x = 70 – 10

$\implies{\rm }$ 4x = 60

$\implies{\rm }$ x = 60/4

$\implies{\rm }$ x = 15

So present age of son is 15 years and present age of mother is :-

➠ 3x

➠ 3 × 15 = 45 years

Answer 2

Appropriate Question :

• Mother is three times as old as her son 5 years hence the sum of their ages will be 70 years . Find their present ages .

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Given : Mother is three times as old as her son & After 5 years the sum of their ages will be 70 years .

Exigency To Find : Son's and Mother's Present Ages .

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❍ Let's Consider the Present age of Son be x yrs .

Given that ,

⠀⠀⠀⠀⠀Mother is three times as old as her son .

Therefore,

• Her Mother's age will be 3x .

⠀⠀⠀⠀⠀▪︎ After 5 years their ages :

• Son's age will be : ( x + 5 ) yrs .
• Mother's age will be : ( 3x + 5 ) yrs .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:According \: To \: \: the \: Question \::}}$

⠀⠀⠀⠀⠀━━━ 5 years hence the sum of their ages will be 70 years .

$\qquad:\implies \sf Son's \:age \:after\:5\:yrs\:+ \:Mother's\:age \:after\:5\:yrs\:= 70 \:$

$\qquad:\implies \sf (x + 5 ) \:+ \:( 3x + 5 )\:= 70 \:$

$\qquad:\implies \sf x + 5 \:+ \:3x + 5 \:= 70 \:$

$\qquad:\implies \sf x \:+ \:3x + 5 + 5\:= 70 \:$

$\qquad:\implies \sf 4x + 5 + 5\:= 70 \:$

$\qquad:\implies \sf \:4x + 10\:= 70 \:$

$\qquad:\implies \sf \:4x \:= 70 - 10 \:$

$\qquad:\implies \sf \:4x \:= 60 \:$

$\qquad:\implies \sf \:x =\dfrac{60}{4} \:$

$\qquad:\implies \sf \:x =\cancel {\dfrac{60}{4}} \:$

$\qquad :\implies \frak{\underline{\purple{\:x = 15 \:yrs\: \:}} }\bigstar$

Therefore,

• Son's Present age is = x = 15 yrs .
• Mother's Present age is = 3x = 3 × 15 = 45 yrs .

⠀⠀⠀⠀⠀$\therefore {\underline{ \sf\:Hence,\:Present \:ages\:of\:mother\:and\:son\:are\:\bf 15 \:\& \:45\:yrs\:\sf , \:respectively. \:}}$

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