After deducting commission at `7 1/2`% on first

₹ 50,000 and 5% on balance of sales made by him, an agent remits ₹ 93,750 to his principal. Find the value of goods sold by him.

#### Solution

Agent earns commission at `7 1/2`% i.e. 7.5% on first ₹ 50,000 sales and on balance, at 5%.

Let total sales be ‘x’.

Commission earned on first ₹ 50,000 at 7.5%

`= 7.5/100 xx 50,000`

= ₹ 3,750

Commission earned on balance at 5%

`= (x - 50,000) xx 5/100`

Total commission earned

= Total sales – Amount remitted

= x – 93,750

∴ `(x - 93,750) = 3,750 + 5/100 xx (x - 50,000)`

∴ `(x - 93,750) xx 100 = 3,750 xx 100 + 5(x - 50,000)`

∴ 100x – 93,75,000 = 3,75,000 + 5x – 2,50,000

∴ 100x – 5x = 1,25,000 + 93,75,000

∴ 95x = 95,00,000

∴ x = `(95,00,000)/95`

∴ x = 1,00,000

∴ The value of goods sold by the agent is

₹ 1,00,000.