Question

Two numbers are in the ratio 3: 5. If 9 is subtracted from each, then they are in the ratio of 12 : 23. Find the second number.​

Answer 1

Given :-

• Two numbers are in the ratio 3: 5. If 9 is subtracted from each, then they are in the ratio of 12 : 23.

To find :-

• Second number

Solution :-

• Two numbers are in the ratio = 3: 5.

Let the first number be 3x then second number be 5x

• According to the given condition

If 9 is subtracted from each, then they are in the ratio of 12 : 23.

→ 3x - 9/5x - 9 = 12/23

→ 23(3x - 9) = 12(5x - 9)

→ 69x - 207 = 60x - 108

→ 69x - 60x = 207 - 108

→ 9x = 99

→ x = 99/9

→ x = 11

Hence,

• First number = 3x = 33

• Second number = 5x = 55

Answer 2

Answer :-

• Second number = 55

Given :-

• Two numbers are in the ratio 3 : 5 and 9 is subtracted from each, then they are in the ratio of 12 : 23.

To Find :-

• Second number.

Solution :-

Put x in the ratio

→ Numbers are

• 3x
• 5x

→ 9 subtracted from both

• 3x - 9
• 5x - 9

If 9 is subtracted from each, then they are in the ratio of 12 : 23

According to question :-

3x - 9/5x - 9 = 12/23

⇒ 23 (3x - 9) = 12 (5x - 9)

⇒ 69x - 207 = 60x - 108

⇒ 69x - 60x = - 108 + 207

⇒ 9x = 99

⇒ x = 99/9

⇒ x = 11

Hence,

• First number = 3x = 3 × 11 = 33
• Second number = 5x = 5 × 11 = 55