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
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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 :

• Original number

Solution :

✦ Let the number be 3x and 5x ✦

According to the given condition

✪ Each number is increased by 10 ,the ratio between the new numbers so formed is 5:7

➡ 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 = 5

Hence,

• Required numbers
• First number = 3x = 15
• Second number = 5x = 25

Answer 2

Step-by-step explanation:

Given that, two numbers are such that the ratio between them is 3:5.

Assume that the first number is x and second number is y.

→ x/y = 3/5

→ 5x = 3y

→ 5x - 3y = 0 ..................(1)

If each is increased by 10 ,the ratio between the new numbers so formed is 5:7.

As per given condition,

→ (x + 10)/(y + 10) = 5/7

→ 7(x + 10) = 5(y + 10)

→ 7x + 70 = 5y + 50

→ 7x - 5y + 20 = 0 ...............(2)

Multiply (1) with 5 and (2) with 3

→ 25x - 15y = 0

→ 15y = 25x .............(3)

→ 21x - 15y + 60 = 0

→ 15y = 21x + 60 ..............(4)

On comparing (3) & (4) we get,

→ 25x = 21x + 60

→ 4x = 60

→ x = 15

Substitute value of x in (1/

→ 5(15) = 3y

→ y = 25

Hence, the original number = x/y = 15/25 = 3/5 (in ratio)

• First number = x = 15
• Second number = y = 25