Question

The greatest ratio among the ratios 2 : 3, 5 : 8, 75 : 121 and 40 : 25 is ______.

विकल्प

• 2 : 3

• 5 : 8

• 75 : 121

• 40 : 25

Answer 1

The greatest ratio among the ratios 2 : 3, 5 : 8, 75 : 121 and 40 : 25 is 40 : 25.

Explanation:

We have, `2 : 3 = 2/3, 5 : 8 = 5/8, 75 : 121 = 75/121`

And `40 : 25 = 40/25`

2	3, 8, 121, 25
2	3, 4, 121, 25
2	3, 2, 121, 25
3	3, 1, 121, 25
5	1, 1, 121, 25
5	1, 1, 121, 5
11	1, 1, 121, 1
11	1, 1, 11, 1
	1, 1, 1, 1

∴ The LCM of 3, 8, 121 and 25 is 2 × 2 × 2 × 3 × 5 × 5 × 11 × 11 = 72600

Making the denominator of each ratio equal to 72600, we get

`2/3 = (2 xx 24200)/(3 xx 24200) = 48400/72600`

`5/8 = (5 xx 9075)/(8 xx 9075) = 45375/72600`

`75/121 = (75 xx 600)/(121 xx 600) = 45000/72600`

`40/25 = (40 xx 2904)/(25 xx 2904) = 116160/72600`

On comparing the numerator of the above ratios, i.e., `40/25` is the greatest ratio, i.e., 40 : 25 is the greatest ratio among the given ratios.