A grocery dealer cheats to the extent of 5% while buying as well as selling by using false weight. What is his profit %?

Let the cost of 100 g of grocery = Rs. 100

If he cheats while buying,

He buys 5% more of grocery for the same cost.

⇒ he buys [100 + (5% of 100)] gram of grocery for Rs. 100.

⇒ CP of 105g = Rs. 100 ---(1)

If he cheats while selling,

He sells 5% less of grocery for the same cost.

As the original SP for 100g grocery should be Rs. 100,

After cheating, SP of 95g = Rs. 100 ---(2)

From 1 and 2,

CP of 105g = SP of 95g = Rs. 100

⇒ CP of 1g = 100/105 = Rs. 20/21

SP of 1g = 100/95 = Rs. 20/19

∴ Profit = SP – CP

= (20/19) – (20/21)

= 40/399

∴ Profit% = 100 × Profit/CP

= 100 × (40/399) × 1/(20/21)

= 100 × (40/399) × (21/20)

= 100 × 2/19

= 200/19

Thus, the total profit% is 10.52%