Question

the present ages of prince and saleem are in ratio 5:7. four years from now the ratio of their ages will be 3:4.find the present age?​

Answer 1

The answer is given in the attachment......

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Answer 2

$\bf{\huge{\underline{\boxed{\rm{\blue{Answer:}}}}}}$

$\bf{\underline{\underline{\sf{\red{Given}}}}}$

• The Present ages of Prince and Saleem are in ratio 5:7
• Four years from now the ratio of their ages will be 3:4.

$\bf{\underline{\underline{\sf{\red{To\:find}}}}}$

• Present age of Prince
• Present age of Saleem

$\bf{\underline{\underline{\sf{\red{Solution}}}}}$

Let x be the common multiple of the ratio 5:7

•°• Prince's present age = 5x

Saleem's present age = 7x

$\bf{\underline{\underline{\sf{\red{According\:to\:question}}}}}$

• Four years from now the ratio of their ages will be 3:4.

Ages 4 years from now :-

Prince's age = 5x + 4 years

Saleem's age = 7x + 4 years

Ratio = 3:4

Representing the condition mathematically.

=> $\large\frac{5x+4}{7x+4}$ = $\large\frac{3}{4}$

Cross multiplying,

=> 4 ( 5x + 4) = 3 ( 5x + 4)

=> 20x + 16 = 15x + 12

Transport the terms,

=> 20x - 21x = 12 - 16

=> - x = - 4

=> x = 4

Substitute x = 4 in the values of the ratio.

$\bf{\large{\underline{\boxed{\rm{\purple{Present\:age\:of\:Prince\:=\:5x\:=\:5\times\:4=\:20\:years}}}}}}$

$\bf{\large{\underline{\boxed{\rm{\purple{Present\:age\:of\:Saleem\:=\:7x\:=\:7\times\:4=\:28\:years}}}}}}$

$\bf\huge\underline{Verification}$

For first case :-

• The Present ages of Prince and Saleem are in ratio 5:7

Present age of Prince = x = 20

Present age of Saleem = y = 28

Ratio = 5:7

=> $\large\frac{x}{y}$ = $\large\frac{5}{7}$

=> $\large\frac{20}{28}$ = $\large\frac{5}{7}$

Dividing LHS by 4,

=> $\large\frac{5}{7}$ = $\large\frac{5}{7}$

LHS = RHS.

For second case :-

• Four years from now the ratio of their ages will be 3:4.

Ages 4 years from now :-

Prince = 5x + 4 = 20 + 4 = 24 years

Sameer = 7x + 4 = 28 + 4 = 32 years

Ratio = 3:4

=> $\large\frac{5x+4}{7x+4}$ = $\large\frac{3}{4}$

=> $\large\frac{28}{32}$ = $\large\frac{3}{4}$

Dividing LHS by 8,

=> $\large\frac{3}{4}$ = $\large\frac{3}{4}$

LHS = RHS

Hence verified.