Question

X and Y are partners. X draws a fixed amount at the beginning of every month. Interest on drawings is charged @8% p.a. At the end of the year interest on X’s drawings amounts to Rs.2,600. Drawings of A’were

Answer 1

Given:

X and Y are partners

X draws a fixed amount at the beginning of every month

Interest on drawings is charged @8% p.a.

At the end of the year interest on X’s drawings amounts to Rs.2,600

To find:

Drawings of X were?

Solution:

Let's assume Rs. "x" as the amount of per month drawing of X.

No. of drawings in a year = 12

∴ The total drawings made by X in a year = Rs. (12x)

The rate of interest = 8 %

Since the amount is withdrawn at the beginning of every month for 12 months, so we can calculate the average period of drawings as:

Average Time is,

=  $\frac{[Time \:left\:after\:1st \:drawing]\:+\:[Time \:left\:after\:last \:drawing]}{2}$

=   $\frac{12\:+\:1}{2}$

=   $\frac{13}{2}$

=   $6.5\:months$

Now, we will use the following formula to find the interest:

$Interest\:on\:drawings = [Annual\:drawings] \times [Rate\:of \:interest]\times [\frac{Average \:Time}{12} ]$

By substituting the values of Interest = Rs. 2600, Annual drawings = 12x, the rate of interest = 8%, in the above formula of interest, we get

$2600 = [12x] \times[\frac{8}{100} ] \times [\frac{6.5}{12} ]$

$\implies 2600\times100\times 12 = 12x\times 8 \times 6.5$

$\implies 3120000 =624x$

$\implies x = \frac{3120000}{624}$

$\implies \bold{x = 5000}$

Thus, the fixed amount of drawings of X at the beginning of every month were Rs. 5000.

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