Question

Two numbers are in the ratio 3 : 4; if 6 be added to each terms of the ratio, then the new ratio

will be 4 : 5, then the numbers are

(a) 14, 20 (b) 17, 19 (c) 18 and 24 (d) none of these​

Answer 1

Answer:

c) 18 and 24

Step-by-step explanation:

18 and 24

18:24 = 3:4

Adding 6 to both numbers

24:30 i.e 4:5

Hence both conditions are satisfied therefore answer is 18 and 24

Answer 2

The numbers are 18 and 24

Step-by-step explanation:

Let,

First number = 3x

Second number = 4x

If 6 be added to each terms of the ratio

First number = 3x + 6

Second number = 4x + 6

Also,

The new ratio will be 4 : 5

So,

$\dfrac{3x \: + \: 6}{4x \: + \: 6} \: = \: \dfrac{4}{5}$

⇒ 5 (3x + 6) = 4 (4x + 6)

⇒ 15x + 30 = 16x + 24

⇒ 15x - 16x = 24 - 30

⇒ - x = - 6

⇒ x = 6

• First number = 3x
• 3 (6) = 18

• Second number = 4x
• 4 (6) = 24

∴ Option (c). 18 and 24

The numbers are 18 and 24