**Question 1. A student buys a pen for Rs. 90 and sells it for Rs. 100. Find his gain and gain percent?**

**Solution:**

Given, the Cost price of pen = Rs 90

The Selling price of pen = Rs 100

Here, Selling price > Cost price

So, there is a Profit or Gain.

So, Gain = Selling price – Cost price = 100 – 90 = Rs 10

And, Gain % = (Gain/Cost price) × 100 = (10/90) × 100 = 100/9 or 11.12 %

Hence, the gain of a person is Rs 10 and the gain percentage is 100/9 or 11.12 %

**Question 2. Rekha bought a saree for Rs. 1240 and sold it for Rs. 1147. Find her loss and loss percent?**

**Solution:**

Given, the Cost price of saree = Rs 1240

The Selling price of saree = Rs 1147

Here, Cost price > Selling price

So, there is a Loss.

So, Loss = Cost price – Selling price = 1240 – 1147 = Rs 93

And, Loss % = (Loss/Cost price) × 100 = (93/1240) × 100 = 7.50%

Hence, Rekha had a loss of Rs 93 and her loss percentage is 7.5 %

**Question 3. A boy buys 9 apples for Rs. 9.60 and sells them at 11 for Rs. 12. Find his gain or loss percent?**

**Solution:**

Given, the Cost price of 9 apples = Rs 9.60

So, the Cost price of 1 apple = Rs 9.60/9 = Rs 1.066

The Selling price of 11 apples = Rs 12

So, the Selling price of 1 apple = Rs 12/11 = Rs 1.090

Here, Selling price > Cost price

So, there is a Profit or Gain.

So, Gain = Selling price – Cost price = 12/11 – 9.60/9 = Rs 0.024

And, Gain % = (Gain/ Cost price) × 100 = (0.024/1.066) × 100 = 2.27 %

Hence, the gain of the boy is Rs 0.024 and the gain percentage is 2.27 %

**Question 4. The cost price of 10 articles is equal to the selling price of 9 articles. Find the profit percent?**

**Solution:**

Given, The cost price of 10 articles = the selling price of 9 articles

Let us takexbe the Cost price of 1 article

Then, the Cost price of 10 articles will be 10x

So, the Selling price of 9 articles will be 10x

And, the Selling price of 1 article will be 10x/9

So, we can say Profit or Gain = Selling price – Cost price = 10x/9 – x = x/9

And, Profit % = (Profit/ Cost price) × 100 = (x/9)/x × 100 = 100/9 = 11.11 %

Hence, the profit percentage is 11.11 %

**Question 5. A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. If he sells the radio for Rs 300, determine his profit percent?**

**Solution:**

Given, the Cost price of radio = Rs 225Overhead

expenses is of Rs 15

So, total Cost price of radio will be Rs 225 + Rs 15 = Rs 240

The Selling price of radio = Rs 300

So, Profit = Selling price – Cost price = 300 – 240 = Rs 60

And, Profit % = (Profit/ Cost price) × 100 = (60/240) × 100 = 25 %

Hence, the profit percentage is 25 %

**Question 6. A retailer buys a cooler for Rs 1200 and overhead expenses on it are Rs 40. If he sells the cooler for Rs 1550, determine his profit percent?**

**Solution:**

Given, the Cost price of cooler = Rs 1200Overhead

expenses is of Rs 40

So, total Cost price of cooler will be Rs 1200 + Rs 40 = Rs 1240

The Selling price of cooler = Rs 1550

So, Profit = Selling price – Cost price = 1550 – 1240 = Rs 310

And, Profit % = (Profit/ Cost price) × 100 = (310/1240) × 100 = 25 %

Hence, the profit percentage is 25 %

**Question 7. A dealer buys a wristwatch for Rs 225 and spends Rs 15 on its repairs. If he sells the same for Rs 300, find his profit percent?**

**Solution:**

Given, the Cost price of wristwatch = Rs 225

Money spent on repairing the watch is Rs 15

So, total Cost price of wristwatch will be Rs 225 + Rs 15 = Rs 240

The Selling price of wristwatch = Rs 300

So, Profit = Selling price – Cost price = 300 – 240 = Rs 60

And, Profit % = (Profit/Cost price) × 100 = (60/240) × 100 = 25 %

Hence, the profit percentage is 25 %

**Question 8. Ramesh bought two boxes for Rs 1300. He sold one box at a profit of 20% and the other box at a loss of 12%. If the selling price of both boxes is the same, find the cost price of each box?**

**Solution:**

Given, Ramesh bought two boxes for Rs 1300

Let us takeabe Cost price of 1st box and1300 – abe Cost price of 2nd box.

Since the first box is sold at a profit of 20%

So, the Selling price of 1st box = a + a × 20/100 = Rs 6a/5

And, the second box is sold at a loss of 12%

So, the Selling price of 2nd box = (1300 – a) – (1300 – a) × 12/100 = Rs (28600 – 22a)/25

It is given that the selling price of both boxes is the same

So, Selling price of 1st box = Selling price of 2nd box

6a/5 = (28600 – 22a)/25

6a/5 = 28600 × 25–22× 25a

So, a = 550

So, the Cost price of 1st box = a = Rs 550

And, the Cost price of 2nd box = 1300 – a = Rs 750

Hence, the Cost price of 1st box is Rs 550 and the Cost price of 2nd box is Rs 750

**Question 9. If the selling price of 10 pens is equal to **the **cost price of 14 pens, find the gain percent?**

**Solution:**

Given, The Selling price of 10 pens = the Cost price of 14 pens

Let us takeabe the Cost price of 1 pen

Then, the Cost price of 14 pens will be 14a

So, the Selling price of 10 pens will be 14a

And, the Selling price of 1 pen will be 14a/10

So, we can say Profit or Gain = Selling price – Cost price = 14a/10 – a = 4a/10

And, Gain % = (Gain/ Cost price) × 100 = (4a/10)/a × 100 = 40 %

Hence, the gain percentage is 40 %

**Question 10. If the cost price of 18 chairs be equal to **the **selling price of 16 chairs, find the gain or loss percent?**

**Solution:**

Given, The Cost price of 18 chairs = The Selling price of 16 chairs

Let us takeabe the Cost price of 1 chair

Then, the Cost price of 18 chairs will be 18a

So, the Selling price of 16 chairs will be 18a

And, the Selling price of 1 chair will be 18a/16

We can clearly see that there is a profit

So, we can say Profit or Gain = Selling price – Cost price = 18a/16 – a = a/8

And, Gain % = (Gain/ Cost price) × 100 = (a/8)/a × 100 = 12.5 %

Hence, the gain percentage is 12.5 %