The number that must be added to each of the | vedclass

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Question

(A) Let the number to be added be $x$.According to the problem,the ratio of the first two numbers becomes equal to the ratio of the last two numbers:$

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(A) Let the number to be added be $x$.According to the problem,the ratio of the first two numbers becomes equal to the ratio of the last two numbers:$\frac{8+x}{21+x} = \frac{13+x}{31+x}$Cross-multiplying the terms:$(8+x)(31+x) = (13+x)(21+x)$$248 + 8x + 31x + x^2 = 273 + 13x + 21x + x^2$$248 + 39x = 273 + 34x$Subtract $34x$ from both sides:$248 + 5x = 273$Subtract $248$ from both sides:$5x = 273 - 248$$5x = 25$$x = 5$Therefore,the required number is $5$.

The number that must be added to each of the numbers $8, 21, 13$ and $31$ to make the ratio of the first two numbers equal to the ratio of the last two numbers is:

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