Question

solve the problem
the age of Rahul and haroon are in the ratio 5:7. Four years later the sum of there age is 56. what are their present age
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Answer 1

✬ Rahul's Age = 20 Years ✬

✬ Haroon's Age = 28 Years ✬

Step-by-step explanation:

Given:

• Age of Rahul and Haroon are in ratio 5:7.
• After 4 years sum of there ages is 56.

To Find:

• Present ages of both ?

Solution: Let the present age of Rahul and Haroon be x and y years respectively. Therefore,

➟ Rahul's age/Haroon's age = 5/7

➟ x/y = 5/7

➟ 7x = 5y

➟ x = 5y/7ㅤㅤㅤㅤㅤ(eqⁿ i )

A/q , After 4 year their ages and sum will be

• Rahul's age = (x + 4) years

• Haroon's age = (y + 4) years

• Sum = 56 years

$\implies{\rm }$ x + 4 + y + 4 = 56

$\implies{\rm }$ x + y = 56 – 8

$\implies{\rm }$ 5y/7 + y = 48

$\implies{\rm }$ 5y + 7y/7 = 48

$\implies{\rm }$ 12y = 48 × 7

$\implies{\rm }$ y = 336/12

$\implies{\rm }$ y = 28

So present age of Haroon is 28 years and age of Rahul is x :-

➮ x = 5 × 28/7

➮ x = 5 × 4

➮ x = 20 years

Hence, present age of Rahul is 20 years.

Answer 2

❍ Let's Consider the Present age of Rahul and Haroon be 5x & 7x , respectively .

⠀⠀⠀⠀⠀After Four years their ages :

• Age of Rahul will be : ( 5x + 4 )
• Age of Haroon will be : ( 7x + 4 )

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:According \: To \: \: \: question\::}}$

━━━ Four years later the sum of there age is 56.

$\qquad :\implies \sf Rahul's \:age \:after \:4\:years \:+ \:Haroon's \:age \:after \:4\:years = 56 \:$

$\qquad :\implies \sf (5x + 4) \:+ \:(7x + 4) = 56 \:$

$\qquad :\implies \sf 5x + 4 \:+ \:7x + 4 = 56 \:$

$\qquad :\implies \sf 5x + 7x \:+ \:4 + 4 = 56 \:$

$\qquad :\implies \sf 12x \:+ \:8 = 56 \:$

$\qquad :\implies \sf 12x \: = 56 - 8\:$

$\qquad :\implies \sf 12x \: = 48\:$

$\qquad :\implies \sf x \: = \dfrac{48}{12}\:$

$\qquad :\implies \sf x \: = \cancel {\dfrac{48}{12}}\:$

$\qquad \longmapsto \frak{\underline{\purple{\:x = 4 \:yrs \: }} }\bigstar$

Therefore,

• Rahul's Present age is : 5x = 5(4) = 20 yrs
• Haroon's Present age is : 7x = 7(4) = 28 yrs

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \sf\:Present \:ages\:of\:Rahul \:and\:are\:\:\bf 20 \:yrs\:\& \;28\:yrs\:\sf, respectively\:.}}$

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V E R I F I C A T I O N :

Given ,

• Four years later the sum of there age is 56.

As , We know that ,

• Present age of Rahul is 20 yrs .
• Present age of Haroon is 28 yrs .

Now ,

$\qquad :\implies \sf Rahul's \:Present \:age \:+ 4 \:+ \:Haroon's \:Present \:age +\:4\: = 56 \:$

$\qquad :\implies \sf 20 \:+ 4 \:+ \:28 +\:4\: = 56 \:$

$\qquad :\implies \sf 24 \:+ \:32\: = 56 \:$

$\qquad :\implies \bf \:56 = 56 \:$

⠀⠀⠀⠀⠀$\therefore {\underline {\bf{ Hence, \:Verified \:}}}$

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