Question

1. Evan withdrew a fixed amount at the end of each
quarter. If interest on his drawings during 2019-20
@10% p.a. amounts to 33,000, then find the amount
of his quarterly drawings.​

Answer 1

ANSWER :

• ❖ If Evan withdrew a fixed amount at the end of each quarter and interest of his drawings during the year 2019-20, @10% p.a. amounts to Rs. 33,000; then his quarterly drawings was Rs. 2,20,000.

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SOLUTION :

❒ Given :-

• Evan withdrew a fixed amount at the end of each quarter.

• Interest on drawing during the year 2019-20, @10% p.a. amounts to Rs. 33,000.

❒ To Find :-

• The amount of Evan's quarterly drawings = ?

❒ Required Formula :-

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

❒ Note :-

• ✎ A year has 4 quarters. Hence, when a fixed amount is withdrawn as drawings every quarter, then the total drawings is calculated by multiplying the fixed amount with 4; i.e., 4 × Fixed Amount = Total Drawings.

• ✎ When equal amounts are withdrawn in the end of each quarter during the year the interest on drawing will be calculated on the total drawings at the specified rate for the average period of 4½ months or 4.5 months.

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❒ Calculation :-

Here,

• Interest on Drawings = Rs. 33,000

• Rate of Interest on Drawings = 10% p.a.

• Time = 4.5 months

Suppose,

• The total drawings of the year 2019-20 = Rs. P

Using the formula of Interest on Drawings, we get,

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

⇒ 33,000 = P × 10% × 4.5 months

⇒ 33,000 = P × $\rm{\dfrac{10}{100}}$ × $\rm{\dfrac{4.5}{12}}$

⇒ 33,000 = P × $\rm{\dfrac{1}{10}}$ × $\rm{\dfrac{4.5}{12}}$

⇒ 33,000 = P × 0.0375

⇒ P × 0.0375 = 33,000

⇒ P = $\rm{\dfrac{33,000}{0.0375}}$

⇒ P = Rs. 8,80,000

• Total Drawings of the year = Rs. 8,80,000

Now,

• A year has 4 quarters.

Suppose,

• The quarterly drawings = Rs. X

Thus,

• ✪ Quarterly Drawings × 4 = Total Drawings

➨ X × 4 = 8,80,000

➨ X = $\rm{\dfrac{8,80,000}{4}}$

∴ X = 2,20,000

• Hence, the amount of quarterly drawings is Rs. 2,20,000.