Question 55

Three numbers are in the ratio $$\frac{1}{2} : \frac{2}{3} : \frac{3}{4}$$. The difference between the greatest and the smallest number is 27. The smallest number is:

Solution

$$\frac{1}{2} : \frac{2}{3} : \frac{3}{4}$$

$$\frac{1}{2}*12 : \frac{2}{3} *12: \frac{3}{4}$$*12

$$6 : 8 : 9$$

Let the numbers are 6x, 8x and 9x

By the problem 9x - 6x = 27

i.e x =9

hence the smallest number is 6x i.e 54

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