Question

Two numbers are such that the ratio between them is 3:5 .If each is increased by 10 the ratio between the new numbers so formed is 5:7
Find the original numbers.​

Answer 1

Given :-

• Two numbers are such that the ratio between them is 3:5
• If each is increased by 10 the ratio between the new numbers so formed is 5:7

To Find :-

• The Original Numbers

Solution :-

⟼ Let the First Number be 3x

⟼ Let the Second Number be 5x

❑ After Increasing the Number by 10

⟼ Let the First Number be 3x + 10

⟼ Let the Second Number be 5x + 10

♱ According to the Question ♱

➞ 3x + 10 / 5x + 10 = 5 / 7

➞ 7 (3x + 10) = 5 (5x + 10)

➞ 21x + 70 = 25x + 50

➞ 21x - 25x = 50 - 70

➞ - 4x = - 20

➞ x = 20/4

➞ x = 5

________________

Therefore :-

• First Number = 3x = 3 × 5 = 15
• Second Number = 5x = 5 × 5 = 25

________________

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Answer 2

Let the numbers be 3x and 5x.

According to the question we can write as

➪ ( 3x + 10 ) = ( 5 )

( 5x + 10 ) ( 7 )

On cross multiplying we get

➪ 7( 3x + 10 ) = 5( 5x + 10 )

➪ 21x + 70 = 25x + 50

On rearranging or transposing

➪ 70 – 50 = 25x – 21x

➪ 4x = 20

➪ x = 20 = 5

4

So the numbers are 15 and 25