Question

What is the least number to be subtracted from 11, 15, 21 and 30 each so that resultant numbers become proportional?


a. 1


b. 2


c. 3


d. 4?

Answer 1

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Answer 2

Answer:

c. 3

Step-by-step explanation:

Let x be the number which is subtracted from 11, 15, 21 and 30 each so that resultant numbers become proportional,

That is,

$\frac{15-x}{11-x}=\frac{21-x}{15-x}=\frac{30-x}{21-x}$

If $\frac{15-x}{11-x}=\frac{21-x}{15-x}$

$(15-x)^2 = (11-x)(21-x)$

$225 + x^2 - 30x = 231 - 11x - 21x + x^2$

$225 - 30x = 231 - 32x$

$2x = 6$

$\implies x = 3$

If x = 3,

$\frac{21-x}{15-x}=\frac{18}{12}=\frac{3}{2}$

$\frac{30-3}{21-3}=\frac{27}{18}=\frac{3}{2}$

Hence, the required number would be 3.

OPTION c is correct.