A trader bought items for ₹1,050 and sold them the same day for ₹1,228.5 at a credit of 10 months, thus gaining 4%. The rate of interest per annum is:

Given:

Cost Price (CP) = ₹1050

Selling Price (SP) = ₹1228.5

Credit period = 10 months

Gain percentage = 4%

Formula Used:

Gain = SP - CP

Gain % = (Gain / CP) × 100

Simple Interest (SI) = (Principal × Rate × Time) / 100

Amount (A) = Principal + SI

In this case, the SP is the amount received after 10 months, which includes the gain and the interest for the credit period on the selling price (assuming the gain was also part of the amount on credit).

Calculation:

Let the actual selling price (without credit) be S.

Gain = S - CP

Gain % = ((S - CP) / CP) × 100

4 = ((S - 1050) / 1050) × 100

4 × 1050 = (S - 1050) × 100

4200 = 100S - 105000

100S = 105000 + 4200

100S = 109200

S = ₹1092

This is the selling price for which the trader gained 4% without any credit period.

The trader sold it for ₹1228.5 at a credit of 10 months. The difference between the credited SP and the actual SP is the interest charged for the credit period on the actual SP.

Interest = ₹1228.5 - ₹1092 = ₹136.5

Here, the Principal for the interest calculation is the actual selling price (S) = ₹1092.

Time (T) = 10 months = 10/12 years

Let the rate of interest per annum be R.

SI = (P × R × T) / 100

136.5 = (1092 × R × (10/12)) / 100

136.5 = (1092 × R × 5) / (100 × 6)

136.5 × 600 = 5460 × R

81900 = 5460 × R

R = 81900 / 5460

R = 15

The rate of interest per annum is 15%.