Question

What number must be added to each term of the ratio 13:16 to become the ratio 4:5

Answer 1

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

▪ What number must be added to each term of the ratio 13: 16 to become the ratio 4 : 5??

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

${ \orange{ \bold{ \underline{Given \: that-}}}}$

=》 original ratio = 13 : 16

${ \bigstar{ \bold{ \underline{according \: to \: the \: question}}}}$

on adding a number to each term of the ratio , the ratio get changed...

=》 new ratio = 4 : 5

▪ Let the number that must be added to the ratio 13 : 16 be x

thus, we get the equation as follows....

${ \bold{ \red{ \implies{ \frac{(13 + x)}{(16 + x)} = \frac{4}{5}}}}}$

▪ cross multiplying both the sides...

${ \purple{ \bold{ \implies{5(13 + x) = 4(16 + x)}}}}$

${ \purple{ \bold{ \implies{65 + 5x = 64 + 4x}}}}$

${ \purple{ \bold{ \implies{5x - 4x = 64 - 65}}}}$

${ \red{ \boxed{ \bold{ \implies{x = - 1}}}}}$

therefore,

-1 must be added to each term of the ratio 13 : 16 to become the ratio 4 : 5

Answer 2

$\huge{\sf{\orange{\underline{SolUtion:-}}}}$

$\star \: {\sf{\underline{\green{Given}}}}$

The original ratio , 13: 16

${\bf{\underline{\green{A.T.Q}}}}$

Adding a number to each term of ratio, the new ratio is

4:5.

Let, x be added to the ratio 13 : 16

NoW,

The equation we can find,....

$\implies{\tt{\green{ \frac{13 + x}{16 + x} = \frac{4}{5}}}}$

${\tt{\pink{By \:cross \: multiplication,}}}$

$\implies{\tt{\blue{5 (13+x) = 4(16+x)}}}$

$\implies{\tt{\blue{65+5x = 64+4x}}}$

$\implies{\tt{\blue{5x- 4x = 64-65}}}$

$\implies{\tt{\blue{x = - 1}}}$

$\large\boxed {\orange{ \: x= -1 }}$

${\tt{\pink{ ∴ \: -1 \: must \: be \: added \: to \: the \: each \: term \: of \: the \: ratio 13 : 16 to \: become \: the \: ratio \: 4:5}}}$