Question

16. Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, the ratio
the digits becomes 4:5 find the number
​

Answer 1

Answer:

Step-by-step explanation:

let  the common multiple be x

therefore the numbers are 5x and 6x

if 8 is subtracted from each, their ratio becomes 4:5

$\frac{5x-8}{6x-8}=\frac{4}{5}\\\\5(5x-8)=4(6x-8)\\\\25x-40=24x-32\\\\x=8$

numbers are 5x and 6x,

that is, 40 and 48

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Answer 2

EXPLANATION.

• GIVEN

Two number are in the ratio of = 5:6

if 8 is subtracted from each of the numbers,

the ratio the digit becomes = 4:5

FIND THE NUMBER.

According to the question,

Let one number be = x

Let another number be = y

Two number = x and y

Case = 1

Two number are in the ratio = 5:6

=> x/y = 5/6

=> 6x = 5y

=> 6x - 5y = 0 .......(1)

Case = 2

if 8 is subtracted from the number the ratio

becomes = 4:5

=> x - 8 / y - 8 = 4/5

=> 5 ( x - 8 ) = 4 ( y - 8 )

=> 5x - 40 = 4y - 32

=> 5x - 4y = 8 ........(2)

From equation (1) and (2)

multiply equation (1) by 4

multiply equation (2) by 5

we get,

=> 24x - 20y = 0

=> 25x - 20y = 40

we get,

=> -x = -40

=> x = 40

put x = 40 in equation (1) we get,

=> 6(40) - 5y = 0

=> 240 - 5y = 0

=> 5y = 240

=> y = 48

Therefore,

The number are = 40 and 48