Question

Out of ratio 7:15,15:23,17:25,21:29 the smallest one is......?

Answer 1

Given :  Ratios 7:15,15:23,17:25,21:29  

To Find :  Smallest  Ratio

Solution:

7:15

15:23

17:25

21:29

To compare lets have same denominator  15 * 23 * 25 * 29

7:15   = 7 * 23 * 25 * 29  /   15 * 23 * 25 * 29

15:23 = 15 * 15 * 25 * 29 /   15 * 23 * 25 * 29

17:25 = 17 * 15 * 23 * 29  /  15 * 23 * 25 * 29

21:29 = 21 *  15 * 23 * 25  / 15 * 23 * 25 * 29

7 * 23 * 25 * 29 = 1,16,725

15 * 15 * 25 * 29 = 1,63,125

17 * 15 * 23 * 29 = 1,70,085

21 *  15 * 23 * 25  = 1,81,125

1,16,725 is smallest

Hence  7:15   is smallest ratio

other way

7:15,  = (7.5 - 0.5)/15 = 1/2 - 0.5/15  < 1/2

15:23 = ( 10.5 + 4.5)/23 = 1/2 + 4.5/23 > 1/2

17:25 = (12.5 + 4.5)/25 =  1/2 + 4.5/25 > 1/2

21:29 = (14.5 + 6.5)/29  = 1/2 + 6.5/29  > 1/2

Hence only 7: 15 is less than 1/2  all others are above 1/2

Hence 7:15 is the smallest ratio

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