Question

two number are in the ratio 5:6 if 8 subtracted from each of the number of ratio because 4:5 find the number​

Answer 1

Answer:

The two numbers = 40 & 48.

Step-by-step explanation:

$\sf \green{Given:- }$

$\bull$ Two number are in the ratio 5:6 if 8 subtracted from each of the number of ratio becomes 4:5.

$\sf \green{To\: Find:-}$

$\bull$ The numbers

$\sf\green{Solution:-}$

$\red{\bold{Let,}}$

• The two numbers be 5x and 6x

$\bigstar \: \sf \: Number \: after \: subtracting \: 8\\ \downarrow \\➳ \: \bf Firs t \: number =5x - 8 \\ ➳ \: \bf Second \: number = 6x - 8 \\ \\ \\ {\red{ \clubs}} \: \rm Req. \: fraction = \frac{4}{5} \\ \\ \\ \green{ \clubs} \: \rm \: After\: fraction = \frac{5x - 8}{6x - 8}$

ACQ,

$\therefore \tt \: \frac{5x - 8}{6x - 8} = \frac{4}{5} \\ \\ ➟ \tt \: 5(5x - 8) = 4(6x - 8) \\ \\ ➟ \tt \: 25x - 40 = 24x - 32 \\ \\ ➟ \tt \: 25x - 24x = - 32+ 40 \\ \\ \tt \: ➟ \huge \pink{\underline{ \boxed{ \frak{\: x = 8}}}}$

$\sf \: ❒ \: First \: number \\⇨ \: \sf 5x \\ ⇨ \sf \: 5 \times 8 \\⇨ \bf \: 40 \\ \\ ❏ \sf \: Second \: number \\ ⇨ \sf \: 6x \\ \sf \: ⇨6 \times 8\\ ⇨ \bf \: 48$

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$\bf \: Verification - \\ \\ ✏ \: \: \sf\frac{5x - 8}{6x - 8} = \frac{4}{5} \\ \\✏ \sf \: \frac{5(8) - 8}{6(8) - 8} = \frac{4}{5} \\ \\ ✏ \tt \: \frac{40 - 8}{48 - 8} = \frac{4}{5} \\ \\ ✏ \tt \: \frac{32}{40} = \frac{4}{5} \\ \\ ✏ \tt \: \cancel{ \frac{32}{40}} = \frac{4}{5} \\ \\ ✏\tt \: \frac{4}{5} = \frac{4}{5} \\ \\ \underline{ \large \purple{\frak{Hence \: Proved}}}$

Answer 2

Let two numbers be x & y

∴$\dfrac{x}{y}$=$\dfrac{5}{6}$

[cross multiplication]

6x-5y=0$\sf \pink{[step \ 1]}$

If 8 is subtracted from both the numbers, the ratio is 4:5

$\dfrac{(x-8)}{y-8}$=$\dfrac{4}{5}$

$\sf\implies$ 5(x-8)=4(y-8)

$\sf\implies$5x-40=4y-32

$\sf\implies$5x-4y=8$\sf \pink{[step \ 2]}$

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Multiplying equation(1) by 4 & equation (2) by 5

we have,

24x-20y=0..$\sf \pink{[step \ 3]}$

25x-20y=40..$\sf \pink{[step \ 4]}$

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Subtract equation (3) from (4)

we have,

x=40

Now,

Substuting the value x=40 in equation (1),we have

6×40-5y=0

$\sf\implies$ 240-5y=0

$\sf\implies$ 240=0+5y

$\sf\implies$240=5y

$\sf\implies$ $\dfrac{240}{5}$

$\sf\implies=\dfrac{\cancel{240}48}{\cancel{5}}$

$\sf\implies$48=y

$\sf\implies$ y=48

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Hence the two numbers are 40 & 48