Question 75

When x is subtracted from each of the numbers 54, 49, 22 and 21, the numbers so obtained are in proportion. The ratio of (8x - 25) to (7x - 26) is:

Solution

According to the problem,

$$\left(54-x\right)\left(21-x\right)=\left(49-x\right)\left(22-x\right)$$

$$1134-75x+x^2=1078-71x+x^2$$

$$4x=56$$

$$x=14$$

$$\left(8x-25\right):\left(7x-26\right)=8\left(14\right)-25\ :\ 7\left(14\right)-26$$

= 87 : 72

= 29 : 24

Hence, the correct answer is Option C

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