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A man buys a watch for Rs. 1950 in cash and sells it for Rs. 2200 at a credit of 1 year. If the rate of interest is 10% per annum, the man:
(a) Gains Rs. 55
(b) Gains Rs. 50
(c) Loses Rs. 30
(d) Gains Rs. 30

Answer Verified Verified
Hint: First, find the true discount after one year using the formula: $TD=\dfrac{SP\times Rate\times Time}{100+\left( Rate\times Time \right)}$. Subtract this true discount from the selling price to find the present worth. In turn, subtract the cost price from this present worth to find the profit or loss which is the final answer.

Complete step-by-step answer:
In this question, we are given that a man buys a watch for Rs. 1950 in cash and sells it for Rs. 2200 at a credit of 1 year. The rate of interest is 10% per annum.

We need to find out how much the man gains or loses.

We see from the question that the Cost Price, CP is Rs. 1950.

The Selling Price, SP is Rs 2200.

We need to find the True Discount, TD after one year.

To find the True Discount, TD after one year, we will use the following formula:

$TD=\dfrac{SP\times Rate\times Time}{100+\left( Rate\times Time \right)}$

Using the above formula, we find the TD for our case:

$TD=\dfrac{2200\times 10\times 1}{100+\left( 10\times 1 \right)}=\dfrac{22000}{110}=200$

So, the total discount is Rs. 200.

We will now subtract this total discount from the selling price to find the present worth.

So, Present Worth = 2200 – 200 = Rs. 2000

Now, to find his gain or loss, we will subtract the cost price from this present worth.

So, Profit = 2000 – 1950 = 50

So, the man gains Rs. 50

Hence, option (b) is correct.

Note: In this question, it is very important to know that the formula for True Discount is $TD=\dfrac{SP\times Rate\times Time}{100+\left( Rate\times Time \right)}$. It is also important to know that we have to subtract the total discount from the selling price to find the present worth and that we have to subtract the cost price from the present worth to find the profit or loss.
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