Question

What number should be subtracted from each of the numbers 23, 30, 57 and 78 so that the resultant numbers are in proportion ?

• A. 4
• B. 3
• C. 6
• D. 7

Answer 1

Answer:

C. 6

The number that should be subtracted is 6.

Let the number to be subtracted from each term be $x$.

According to the problem, the resulting numbers $(23-x)$, $(30-x)$, $(57-x)$, and $(78-x)$ must be in proportion:
$\frac{23 - x}{30 - x} = \frac{57 - x}{78 - x}$

Step 1: Cross-multiply the fractions
$(23 - x)(78 - x) = (57 - x)(30 - x)$

Step 2: Expand both sides

• Left side: $1794 - 23x - 78x + x^2 = 1794 - 101x + x^2$

• Right side: $1710 - 57x - 30x + x^2 = 1710 - 87x + x^2$

Now set them equal:
$1794 - 101x + x^2 = 1710 - 87x + x^2$

Step 3: Simplify and solve for $x$
Cancel $x^2$ from both sides:
$1794 - 101x = 1710 - 87x$

Rearrange the terms to bring $x$ to one side:
$1794 - 1710 = -87x + 101x$
$84 = 14x$
$x = \frac{84}{14} = 6$