Question

the ages of Rahul and haroon are in ratio 5:7 . four years later sum of their ages will be 56 years . what are their present ages?​

Answer 1

Given :

• Ratio of Rahul and Haroon age = 5 : 7

• Four years later sum of their ages = 56 yrs

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To find :

• The present age of Rahul and Haroon.

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Assumption :

Let the common term in the given ratio be x.

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Solution :

From Criteria 1 in given -

Ratio of Rahul and Haroon age = 5 : 7

Therefore,

• Age of Rahul = 5x

• Age of Haroon = 7x

Calculating their age after four years -‎

• Age of Rahul after 4 years = ( 5x+4 )

• Age of Haroon after 4 years = ( 7x+4 )

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From Criteria 2 in given -

Four years later sum of their ages = 56 yrs

$\tt\:(5x+4)+(7x+4)=56$

Opening the brackets

$\tt\implies\:5x+4+7x+4=56$

Arranging the numbers

$\tt\implies\:5x+7x+4+4=56$

Proceeding with simple calculations

$\tt\implies\:12x+4+4=56$

$\tt\implies\:12x+8=56$

Transposing +8 to RHS it becomes -8

$\tt\implies\:12x=56-8$

$\tt\implies\:12x=48$

Transposing 12 to RHS it goes to the denominator

$\tt\implies\:x=\frac{48}{12}$

Reducing the fraction

$\tt\implies\:x=\cancel{\frac{48}{12}}$

$\small{\underline{\boxed{\mathrm{\implies\:x\:=\:4\:yrs}}}}$

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Calculating the age of Rahul and Haroon by pugging the values of x as 4 in the assumed ages :

❒ Present age of Rahul = 5 × 4 = $\large{\mathfrak\red{20~yrs}}$

❒ Present age of Haroon = 7 × 4 = $\large{\mathfrak\red{28~yrs}}$

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Verification :

According to question -

$\tt\:(5x+4)+(7x+4)=56$

$\tt\dashrightarrow\:(5 \times 4+4)+(7 \times 4+4)=56$

$\tt\dashrightarrow\:(20+4)+(28+4)=56$

$\tt\dashrightarrow\:20+4+28+4=56$

$\tt\dashrightarrow\:24+28+4=56$

$\tt\dashrightarrow\:52+4=56$

$\tt\dashrightarrow\:56=56$

$\bf\dashrightarrow\:LHS~=~RHS$

Hence Verified!~

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Henceforth,

The present age of Rahul and Haroon are 20yrs and 28yrs respectively.

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$\tt\color{maroon}{~~~~~~~~~~~~~~~~~~~~~~~~“~Thank~uH~\heartsuit~”~}$

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Answer 2

ANSWER:-

Rahul present age -20

Haroon  present age -28

QUESTION:-

The age of Rahul and Haroon are in the ratio 5:7. Four years later the sum of ages will be 56 years. What are their present ages?

GIVEN:-

• Ratio of their ages
• Four yeas later sum of their ages

TO FIND:-

THEIR PRESENT AGE

$\huge\mathfrak\pink{Explanation}$

Let the present age of Rahul be 5x

and of Haroon be 7x

Four year later their ages will be,

Rahul-5x+4

Haroon-7x+4

ATQ,

AFTER 4 YEARS THE SUM OF AGES WILL BE 56

S0,

5x+4+7x+4=56

12x+8=56

12x=48

x=48/12

x=4

SO Rahul present age is 5x==>5×4=20

and Haroon present age is 7x==>7×4=28

VERIFICATION:-

AFTER 4 YEARS SUM OF THEIR AGES IS 56

SO Rahul age after 4 years =20+4

==>24 years

Haroon age after 4 years =28+4

==>32 years

Now sum of their ages will be :-

24+32= 56 years

Hence,verified