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Question
The greatest ratio among the ratios 2:3, 5:8, 75:121 and 40:25 is ______.
Options
2:3
5:8
75:121
40:25
Solution
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)/(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.
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