Question 57

If x is subtracted from each of 24, 40, 33 and 57, the numbers, so obtained are in proportion. The ratio of (5x + 12) to (4x + 15) is:

Solution

According to the problem,

$$\left(24-x\right)\left(57-x\right)=\left(40-x\right)\left(33-x\right)$$

$$1368-81x+x^2=1320-73x+x^2$$

$$8x=48$$

$$x=6$$

The ratio of (5x + 12) to (4x + 15) = 5(6) + 12 : 4(6) + 15

= 42 : 39

= 14 : 13

Hence, the correct answer is Option C

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