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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