Question

Two numbers are in the ratio 4 : 5. if 5 is added to each number, the ratio becomes 13 : 16. Find the number?​

Answer 1

$\huge{\bold{\underline{\underline{Question:-}}}}$

Two numbers are in the ratio 4 : 5. if 5 is added to each number, the ratio becomes 13 : 16. Find the number?

$\huge{\bold{\underline{\underline{Solution:-}}}}$

Let one number be '4x'

Let other number be '5x'

A.T.Q.

$= > \frac{4x + 5}{5x + 5} = \frac{13}{16}$

By cross multiplication,

$= > 16(4x + 5) = 13(5x + 5)$

$= > 64x + 80 = 65x + 65$

$= > 80 - 65 = 65x - 64x$

$= > x = 15$

Verification :-

Putting the value of 'x'

$= > \frac{4(15) + 5}{5(15) + 5} = \frac{13}{16}$

$= > \frac{60 + 5}{75 + 5} = \frac{13}{16}$

$= > \frac{65}{80} = \frac{13}{16}$

$= > \frac{ \cancel {65}}{ \cancel {80}} = \frac{13}{16}$

$= > \frac{13}{16} = \frac{13}{16}$

Since, $\frac{13}{16}$ can be written as 13:16

∴ 13:16 = 13:16

Since, L.H.S. = R.H.S.

Hence proved