Question

Two numbers are in the ratio 4:5. If 4
is added to each term, the ratio becomes
25: 31 Find the original numbers.​

Answer 1

Answer:

${ \huge \sf{ \pink{Solution:}}}$

Ratio of numbers = 4:5

Let us take numbers = 4x : 5x

By adding 4,

$: { \implies{ \sf{ \frac{4x + 4}{5x + 4} = \frac{25}{31} }}} \\ \\ : { \implies{ \sf{31(4x + 4) = 25(5x + 4)}}} \\ \\ : { \implies{ \sf{124x + 124 = 125x + 100}}} \\ \\ : { \implies{ \sf{125x - 124x = 124 - 100}}} \\ \\ : { \implies{ \sf{1x = 24}}} \\ \\ : { \implies{ \sf{x = 24}}}$

$\: : { \implies{ \sf{3x = 3(24) = 72}}} \\ \\ : { \implies{ \sf{4x = 4(24) = 96}}}$

${ \therefore{ \sf{ \red{The \: numbers \: are \: 72,96}}}}$