Question

141 is divided into two parts in such a way that the one-eighth part of the first and one-ninth part of the second are in the ratio 5: 6. Find the first part.

• A. 36
• B. 72
• C. 48
• D. 60

Answer 1

Answer:

D. 60

Let the two parts be x and y.

Given:
$x + y = 141$

According to the question:
$\frac{x}{8} : \frac{y}{9} = 5 : 6$

So,
$\frac{\frac{x}{8}}{\frac{y}{9}} = \frac{5}{6}$
$\frac{x}{8} \times \frac{9}{y} = \frac{5}{6}$
$\frac{9x}{8y} = \frac{5}{6}$

Cross multiply:

$9x \times 6 = 5 \times 8y$
$54x = 40y$
$27x = 20y$
$x = \frac{20}{27}y$

Substitute into (x + y = 141)
$\frac{20}{27}y + y = 141$
$\frac{20y + 27y}{27} = 141$
$\frac{47y}{27} = 141$
$47y = 141 \times 27$
$47y = 3807$
$y = 81$

Now,

$x = 141 - 81 = 60$

First part = 60