**Comparing Quantities**

**Profit & Loss and Simple Interest****Important points**

Simple Interest

1. C.P. = Cost Price (Amount at which goods are purchased)

2. Sales Tax, VAT, cartage etc.are included in cost price.

3. S.P. = Selling Price (Amount at which goods are sold)

4. If SP > CP then it is Profit or Gain. Profit = SP - CP

5. If CP > SP then it is Loss. Loss = CP - SP

6. Profit of Loss per cent is always calculated on the cost price.

7. Similarly SP and CP can be computed as:

Simple Interest

8. Principal (P): Money borrowed or invested is called Principal or sum.

9. Interest: Additional money earned or paid on the invested money.

10. Rate (R%) = Interest on Rs 100 for a year.

11. Simple Interest (SI) = Interest calculated uniformly on the original principal throughout the loan or invested period.

12. Amount = Principal + Interest

13. If P = principal, R = rate% per annum, T = number of years,

SI = P × R × T/100

**NCERT EXERCISE 8.3**

**Q1: Tell what is the profit or loss in the following transactions. Also find profit per cent or loss per cent in each case.**

(a) Gardening shears bought for Rs 250 and sold for Rs 325.

(b) A refrigerater bought for Rs 12,000 and sold at Rs 13,500.

(c) A cupboard bought for Rs 2,500 and sold at Rs 3,000.

(d) A skirt bought for Rs 250 and sold at Rs 150.

Answer:

(a) SP = ₹325

CP = ₹250

Profit = 325 - 250 = ₹

**75**

Profit% = (Profit/CP) × 100 = (75/250) × 100 =

**30%**

(b) SP = ₹13500

CP = ₹12000

SP > CP ⇒ Profit

Profit = 13500 - 12000 = ₹1500

Profit% = (Profit/CP) × 100 =(1500/12000) ×100 =

**₹**

**12.5%**

(c) SP = ₹3000

CP = ₹2500

SP > CP ⇒ Profit

Profit = SP - CP = 3000 - 2500 = ₹500

Profit% = (Profit/CP) × 100 = (500/2500) × 100 =

**20%**

(d) SP = ₹150

CP = ₹250

CP > SP ⇒ Loss

Loss = CP - SP = 250 - 150 = ₹100

Loss% = (Loss/CP) × 100 = (100/250) × 100 =

**40%**

**Q2: Convert each part of the ratio to percentage:**

**(a) 3:1 (b) 2:3:5 (c) 1:4 (d) 1:2:5**

Answer:

(a) 3:1

Total parts = 3 + 1 = 4

1st part in % = (3/4) × 100 = 75%

2nd part in % = (1/4) × 100 = 25%

(b) 2:3:5

Total Parts = 2 + 3 + 5 = 10

1st part = (2/10) × 100 = 20%

2nd part = (3/10) × 100 = 30%

3rd part = (5/10) × 100 = 50%

(c) 1:4

Total Parts = 1 + 4 = 5

1st part = (1/5) × 100 = 20%

2nd part = (4/5) × 100 = 80%

(d) 1:2:5

Total parts = 1 + 2 + 5 = 8

1st part = (1/8) × 100 =12.5%

2nd part = (2/8) × 100 = 25%

3rd part = (5/8) × 100 =62.5%

**Q3: The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.**

Answer: Initial population = 25000

Final population = 24500

Decrease in population = Final Population - Initial Population

= 24500 - 25000 = -500

(-ve value indicates decrease).

Percentage decrease = (decrease/initial value) × 100

= (-500/25000) × 100 =

**-2%**

**Q4: Arun bought a car for Rs 3,50,000. The next year, the price went upto Rs 3,70,000. What was the Percentage of price increase?**

Answer: Initial price of car = ₹ 350000

Increased price of car = ₹ 370000

Actual Increase = Increased Value - Initial Value = 370000 - 350000

= ₹ 20000

Percent Increase = (Actual Increase/Initial Value) × 100

= (20000/350000) × 100 =

**40/7%**

**Q5: I buy a T.V. for Rs 10,000 and sell it at a profit of 20%. How much money do I get for it?**

Answer: CP = ₹ 10000

Profit% = 20

SP = ?

SP = (100 + Profit%) × CP / 100 = (100+20) × 10000/100

= 120 × 100 =

**₹ 12000**

**Q6: Juhi sells a washing machine for Rs 13,500. She loses 20% in the bargain. What was the price at which she bought it?**

Answer: SP of washing machine = ₹ 13500

loss = 20%

CP = ?

CP =[100/(100 - loss%)] × SP = [100/(100 - 20)] × 13500

= (100/80) × 13500 = ₹16875

**Q7: (i) Chalk contains calcium, carbon and oxygen in the ratio 10:3:12. Find the percentage of carbon in chalk.**

**(ii) If in a stick of chalk, carbon is 3g, what is the weight of the chalk stick?**

Answer:

(i) Calcium:Carbon:Oxygen = 10:3:12

Total Parts = 10 + 3 + 12 = 25

Calcium % in Chalk = (10/25) × 100 = 40%

Carbon % in Chalk = (3/25) × 100 = 12%

Oxygen % in Chalk = (12/25) × 100 = 48%

(ii) Weight of Carbon = 3g

Let the weight of chalk = n grams

Carbon % in Chalk = 12%

⇒ 12% of n = 3g

12/100 × n = 3

n = 3 × 100/12 =

**25g**

**Q8: Amina buys a book for Rs 275 and sells it at a loss of 15%. How much does she sell it for?**

Answer: CP of the book = ₹ 275

Loss% = 15%

SP = [(100-loss%)/100] × CP = [(100 - 15)/100] × 275

= 85 × 275/100 = 23375/100 = ₹

**233.75**

**Q9: Find the amount to be paid at the end of 3 years in each case:**

**(a) Principal = Rs 1,200 at 12% p.a.**

**(b) Principal = Rs 7,500 at 5% p.a.**

Answer:

(a) Principal = ₹1200, R = 12% T = 3years

SI = P×R×T/100 = 1200 × 12 × 3 /100 = ₹432

Amount = Principal + SI = 1200 + 432 = ₹

**1632**

(b) Principal = ₹7500, R = 5% and T = 3 years

SI = P×R×T/100 =7500 × 5 × 3/ 100 = ₹1125

Amount = Principal + SI =7500 + 1125 = ₹8625

**Q10: What rate gives Rs 280 as interest on a sum of Rs 56,000 in 2 years?**

Answer: Principal = ₹56000

SI = ₹280

Time (T) = 2 years

Rate (R) = ?

R = (SI × 100)/ (P × T)

= (280 × 100) / (56000 × 2) = 28/(56 x 2) = 1/4 =

**0.25%**

**Q11: If Meena gives an interest of Rs 45 for one year at 9% rate p.a.. What is the sum she has borrowed?**

Answer: SI = ₹ 45

Rate = 9% p.a.

Time = 1 year

Principal = ?

P = (SI × 100)/ (R × T) = (45 × 100)/ (9 × 1) = ₹

**500**

__Misc. Questions__

**Q12: By selling California apples at Rs 384 a kilogram, a shopkeeper incurs a loss of 4%. At what price mush he sell so that he get a profit of 10%**

Answer: SP =₹

__384 and loss = 4%__

CP = [100/(100 - loss%)] × SP

∴ CP = [100/(100 - 4)] × 384

CP = 100/96 × 384 = 100 × 4 = ₹ 400

CP = ₹ 400

Gain = 10%

SP = [(100+gain%)/100] × CP = [(100+10)/100] × 400

= 110/100 × 400 = ₹

**440**

(In progress...)

this is helpful but give harder sums

ReplyDeleteIts good like to see more

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