The document NCERT Solutions(Part- 3)- Comparing Quantities Class 8 Notes | EduRev is a part of the Class 8 Course Class 8 Mathematics by Full Circle.

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** Exercise 8.2**

**Question 1. ****A man got a 10% increase in his salary. If his new salary is Rs 1,54,000, find his original salary.**

**Solution:** Let the original salary = Rs x

∴ Increase in salary = 10% of Rs x

New salary =

∴ Rs 11/10x = Rs 154000

or

Thus, the original salary = Rs 1,40,000

**Question 2.**** On Sunday 845 people went to the Zoo. On Monday only 169 people went. What is the per cent decrease in the people visiting the Zoo on Monday?**

**Solution:**

Number of visitors on Sunday = 845

Number of visitors on Monday = 169

Decrease in the number of visitors = 845 – 169 = 676

∴ Per cent decrease = = (4 * 20)% = 80%

**Question 3.** **A shopkeeper buys 80 articles for Rs 2,400 and sells them for a profit of 16%. Find the selling price of one article.**

**Solution: **Cost price = Rs 2400

Profit = 16% of Rs 2400

= Rs 16 * 24 = Rs 384

∴ Selling price = Rs 2400 + Rs 384 = Rs 2784

Now, selling price per article = Rs 2784/80 [∵ Number of articles = 80]

**Question 4.** **The cost of an article was Rs 15,500. Rs 450 were spent on its repairs. If it is sold for a profit of 15%, find the selling price of the article.**

**Solution:**

Total cost = Rs 15500 + Rs 450 (Overhead expenses)

= Rs 15950

Profit = 15% of Rs 15950

∴ Selling price = Rs 15950 + Rs 2392.50

= Rs 18342.50

**Question 5.** **A VCR and TV were bought for Rs 8,000 each. The shopkeeper made a loss of 4% on the VCR and a profit of 8% on the TV. Find the gain or loss per cent on the whole transaction.**

**Solution:**

**For VCR For TV**

CP = Rs 8000 CP = Rs 8000

Loss = 4% of Rs 8000 Profit = 8% of Rs 8000

∴ SP = Rs 8000 – Rs 320 SP = Rs 8000 + Rs 640

Now, total CP = Rs 8000 + Rs 8000 = 16000

Total SP = Rs 7680 + Rs 8640 = Rs 16320

∵ SP > CP

∴ Overall profit = Rs 16320 – Rs 16000 = Rs 320

Overall profit per cent =

**Question 6.** **During a sale, a shop offered a discount of 10% on the marked prices of all the items. What would a customer have to pay for a pair of jeans marked at Rs 1450 and two shirts marked at Rs 850 each?**

**Solution:**

**For a pair of Jeans For two Shirts **

Marked price = Rs 1450 Marked price = (Rs 850) x 2 = Rs 1700

Discount = 10% of Rs 1450 Discount = 10% of Rs 1700

= Rs 145 = Rs 170

∴ Sale price = Rs 1450 – Rs 145 ∴ Sale Price = Rs 1700 – 170

= Rs 1305 = Rs 1530

Total sale price = Rs 1305 + Rs 1530

= Rs 2835

Thus, the customer would have to pay Rs 2835.

**Question 7.** **A milkman sold two of his buffaloes for Rs 20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss.(Hint: Find CP of each.)**

**Solution:**

**For 1st buffalo For 2nd buffalo**

SP = Rs 20,000 SP = Rs 20,000

Profit = 5% Loss = 10%

Now, Overall SP = Rs 2 * 20,000

= Rs 40,000

Overall CP =

= Rs 41269.84

Now, CP > SP

∴ Overall loss = Rs (41269.84 – 40000)

= Rs 1269.84

**Question 8.** **The price of a TV is Rs 13,000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it.**

**Solution:**

Cost (sale price) of the TV = Rs 13,000

Rate of sales tax = 12%

∴ Sales tax = 12% of Rs 13000

= Rs (12 * 130) = Rs 1560

∴ Bill amount = Rs 13000 + Rs 1560

= Rs 14,560

Thus Vinod will have to pay Rs 14,560 for the TV.

**Question 9.** **Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is Rs 1,600, find the marked price.**

**Solution: **

Let the marked price = Rs 100

∴ Discount = 20% of Rs 100

Sale price = Rs (100 – 20) = Rs 80

If sale price is Rs 80, then marked price = Rs 100

If sale price is Rs 1600, then marked price = Rs 100/80 * 1600 = Rs 2000

**Question 10.**** I purchased a hair-dryer for Rs 5,400 including 8% VAT. Find the price before VAT was added.**

**Solution: **Let the original price = Rs 100

∴ Original price + VAT = Rs 100 + Rs (8% of 100)

= Rs 108

∴ Bill amount = Rs 108

If bill amount is Rs 108, then original price = Rs 100

If bill amount is Rs 5,400, then original price = Rs 100/108 * 5400

= Rs (100 * 50)

= Rs 5000

**Compound Interest**

Interest is the extra money paid by banks, post offices or people when they borrow money. In simple interest, the principal remains the same each year.

Amount = Principal + Interest

**Application of Compound Interest Formula**

The formula A = can use to find:

(i) Increase (or decrease) in population.

(ii) The growth of a bacteria if the rate of growth is known.

(iii) The value of an item, if its price increase or decrease in the intermediate years.

**Example 1. ****A car was purchased for Rs 2,10,000. After 2 years the value of the car depreciated 5%. Find the value of the car after one year.**

Note: Depreciation means reduction of value due to use and age of the item.

**Solution:** We have P = Rs 2,10,000, R = 5% p.a., T = 2 years

∵ Reduction is there, we use the following formula:

∴

= Rs (525 * 19 * 19) = Rs 1,89,525

∴ The value of the car after 2 years = Rs 1,89,525

**Question: ****Find interest and amount to be paid on Rs 15000 at 5% per annum after 2 years.**

**Solution:** Here, Principal = Rs 15000

Rate of interest = 5% per annum

Time = 2 years

∵

∴

= Rs (150 * 5 * 2) = Rs 1500

∵ Amount = P + SI

∴ Amount = Rs 15000 + Rs 1500 = Rs 16500

**Note:**

**I.** When interest is calculated on the amount of previous year then it is called compound interest (CI).

**II.** Unlike simple interest, the formula for compound interest, i.e.

gives us the amount directly.

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