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 *₹2,600. Drawings of A’were :

Answer 1

Answer:

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Since the amount is withdrawn at the beginning of every month for 12 months, so we can calculate the average period of drawings as: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

2

[Timeleftafter1stdrawing]+[Timeleftafterlastdrawing]

= \frac{12\:+\:1}{2}

2

12+1

= \frac{13}{2}

2

13

= 6.5\:months6.5months

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} ]Interestondrawings=[Annualdrawings]×[Rateofinterest]×[

12

AverageTime

]

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} ]2600=[12x]×[

100

8

]×[

12

6.5

]

\implies 2600\times100\times 12 = 12x\times 8 \times 6.5⟹2600×100×12=12x×8×6.5

\implies 3120000 =624x⟹3120000=624x

\implies x = \frac{3120000}{624}⟹x=

624

3120000

\implies \bold{x = 5000}⟹x=5000

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

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Hope it helpful