Question

Two numbers are in the ratio 5:6 if 8 is subtracted from each of the ratio become 4:5. Find the numbres​

Answer 1

Given:-

• Two numbers are in the ratio 5:6
• If 8 is subtracted from each of them, the ratio becomes 4:5

To find:-

• The numbers

Assumption:-

• Let the ratio common be x
• 1st number = 5x
• 2nd number = 6x

Solution:-

According To the Question:-

If we subtract 8 from each number then the ratio will reduce to 4:5

Hence,

(5x - 8) : (6x - 8) = 4 : 5

⇒ (5x - 8)/(6x - 8) = 4/5

By Cross - multiplication

⇒ 5(5x - 8) = 4(6x - 8)

Removing bracket by multiplying

⇒ 25x - 40 = 24x - 32

Bringing constants on RHS and variable on LHS

⇒ 25x - 24x = 40 - 32

⇒ x = 8

Putting the value of x in the ratio whose constant we assumed to be x:-

• 1st number = 5x = 5 × 8 = 40
• 2nd number = 6x = 6 × 8 = 48

Therefore The two numbers are 40 and 48.

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Verification:-

Let us verify if we subtract 8 from each number then the ratio reduces to 4:5 or not.

For 1st number:-

40 - 8 = 32

For 2nd number:-

48 - 8 = 40

Ratio:-

32 : 40

⇒ 32/40

Cancelling both numerator and denominator by 8.

= 4/5 ⇒ 4:5

Therefore we can see the ratio reduces to 4:5.

Hence, Verified!!!

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Answer 2

Answer:

Given :-

• Numbers are in ratio 5:6
• If 8 subtracted from both then the ratio become 4:5

To Find :-

Numbers

Solution :-

Let us assume the number be 5x and 6x

When 8 subtracted

$\sf \: \dfrac{5x - 8}{6x - 8} = \dfrac{4}{5}$

$\sf \: 5(5x - 8) = 4(6x - 8)$

$\sf \: 25x - 40 = 24x - 32$

$\sf \: 24x - 25x = 32 - 40$

$\sf \: - x = - 8$

$\sf \: x \: = 8$

Numbers are :-

$\sf \: \: 5x - 8 = 5(8) = 40$

$\sf \: 6x = 6(8) = 48$