Question

x and y are partners, x draws fixed amount at the end of every month. Interest on drawings is charged @ 15%. p.a. At the end of the year. interest on drawings of y amounts too 4,125. Drawings of x will be. ​

Answer 1

ANSWER :

• ❖ If X and Y are partners , where X draws a fixed amount at the end of every month, interest on drawings is charged @15%. p.a and at the end of the year, interest on drawings of X amounts to Rs. 4,125; then the amount of Total Drawings of X will be Rs. 60,000 and the amount of monthly Drawings of X will be Rs. 5,000.

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SOLUTION :

❒ Given :-

• X withdrew a fixed amount at the end of every month.

• Interest on drawing is charged @15%

• Interest on drawing at the end of the year amounts to Rs. 4,125.

❒ To Find :-

• The amount of X's drawings = ?

❒ Required Formula :-

• $\dag \: \: \underline{ \boxed{ \sf{ \: Interest \: \: on \: \: Drawings = Total \: \: Drawings \times Rate \: \: of \: \: Interest \times Time \: }}}$

❒ Note :-

• ✎ A year has 12 months. Hence, when a fixed amount is withdrawn as drawings every month, then the total drawings is calculated by multiplying the fixed amount with 12; i.e., 12 × Fixed Amount = Total Drawings.

• ✎ When equal amounts are withdrawn in the end of each month during the year the interest on drawing will be calculated on the total drawings at the specified rate for the average period of 5½ months or 5.5 months.

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❒ Calculation :-

Here,

• Interest on Drawings = Rs. 4,125

• Rate of Interest on Drawings = 15% p.a.

• Time = 5.5 months

Suppose,

• The total drawings of the year = Rs. P

Using the formula of Interest on Drawings, we get,

• ★ Interest on Drawings = Total Drawings × Rate of Interest × Time

⇒ 4,125 = P × 15% × 5.5 months

⇒ 4,125 = P × $\rm{\dfrac{15}{100}}$ × $\rm{\dfrac{5.5}{12}}$

⇒ 4,125 = P × 0.06875

⇒ P × 0.06875 = 4,125

⇒ P = $\rm{\dfrac{4,125}{0.06875}}$

∴ P = Rs. 60,000

• Hence, the amount of total drawings of the year = Rs. 60,000

Now,

• A year has 12 months.

Suppose,

• The amount of monthly drawings = Rs. X

Thus,

• ✪ Monthly Drawings × 12 = Total Drawings

➨ X × 12 = 60,000

➨ X = $\rm{\dfrac{60,000}{12}}$

∴ X = 5,000

• Hence, the amount of monthly drawings is Rs. 5,000