Chapter 8: Comparing Quantities

Exercise 8.1

Solution: (a) We have,

The ratio =

(b) We have,

       The ratio =

[Note : 1km = 1000 m ]

(c) We have, 

  The ratio =

[Note : Rs 1 = 100 Paise ]

Solution:  (a)  We have,

(b) We have, 

Solution:  The students are interested in mathematics

 

The students are not interested in mathematics  

Therefore, the percentage of the students

 

Solution:  Total number of matches = 100 .

Therefore, the number of matches

Solution:  Suppose , the money of  Chameli is Rs 100 .

The money spent by Chameli

The money left after spent by chameli = Rs 100 – Rs 75 = Rs 25

Therefore, the money of Chemali in beginning

 

Solution: Total number of people = 50,00,000 .

The percentage of other game = (100 – 60 – 30)% = (100 – 90) % = 10 %

The number people who like cricket

 

The number people who like football

 

The number people who like other game

 

Exercise 8.2

Solution:  Let  be the original salary .

Given, new salary (A) = Rs 154000 and increase in salary (R) = 10 %

We know that, 

Therefore, the original salary is Rs 1,40,000 .

Solution:  Given , the number of visitor on Sunday = 845 and on Monday = 169 .

The decrease the number of visitor = 845 – 169 = 676

The per cent decrease in the people visiting the Zoo on Monday

Solution:  Price of each articles

Now , Profit

Thus , the selling price of one article = Rs (30+4.8) = Rs 34.8

Solution:  The total cost of an article = The cost of an article + The cost of repairs

= Rs (15500 +450) = Rs 15950

Profit

Thus , the selling price of the article = Rs (15950 + 2392.50) = Rs 18342.50

Solution:  Given, Price of a VCR = Rs 8000 and loss 4 % (This means  cost price is Rs 100 , then selling price is Rs (100 – 4) =Rs 96).

Selling price of a VCR

 

 Again , price of a TV = Rs 8000 and profit 8% (This means cost price is Rs 100 , then selling price is Rs (100 + 8) =Rs 108).

Selling price of a VCR

Total cost price = Rs 8000 +Rs 8000 = Rs 16000

And total selling price = Rs 7680 + Rs 8640 = Rs 16320

Since , total SP > total CP

 Profit = Rs (16320 - 16000) = Rs 320

Therefore , the gain percent on the whole transaction

Solution:  Marked price = Cost of a jeans + Cost of two shirts

= Rs 1450 +Rs 2×850

=Rs (1450 + 1700) = Rs 3150

and the discount percentage = 10 %

Discount

 The sale price = Marked price – discount = Rs (3150 – 315) = Rs 2835

Therefore , the customer has to pay Rs 2835 .  

Solution:  The cost price of each buffaloes = Rs 20,000 and gain 5% .

 This means if CP is Rs 100 then SP is Rs (100 + 5 )= Rs 105  .

Selling price

 

Again , the cost price of each buffaloes = Rs 20,000 and loss 10 % .

 This means if CP is Rs 100 then SP is Rs (100 – 10 )= Rs 90 .

The cost price

Total selling price = Rs (20000 + 20000) = Rs 40000

And total cost price = Rs (19047.62 + 22222.22) = Rs 41269.84

Since total cost price > selling price .

Loss  = Rs (41269.84 – 40000) = Rs 1269.84  

Solution: The price of a TV  = Rs 13000 and rate 12% .

On Rs 13000 , the tax paid would be

Therefore, the amount that Vinod will have to pay = The Price of a TV + Sales tax

= Rs (13000 + 1560) = Rs14560

Solution: let the marked price of the skates is Rs 100 .

Then selling price = Rs (100 – 20) = Rs 80

The marked price

    

Solution: Let the original price of the article be Rs 100 and VAT = 8 %

  Price after VAT in including  = Rs 108 .

When the selling price is Rs 118 then original price = Rs 100 .

 When the selling price is Rs 5400 then original price

Therefore, the price before VAT was Rs 5000 .

Solution: Let the original price of the article be Rs 100 and GST = 18 %

Price after GST in included = Rs (100+18) = Rs 118

When the selling price is Rs 118 then original price = Rs 100 .

When the selling price is Rs 1239 then original price

Exercise 8.3

1. Calculate the amount and compound interest on
(a) Rs10,800 for 3 years at  % per annum compounded annually.
(b) Rs 18,000 for   years at 10% per annum compounded annually.
(c) Rs 62,500 for  years at 8% per annum compounded half yearly.
(d) Rs 8,000 for 1 year at 9% per annum compounded half yearly. (You could use the year by year calculation using SI formula to verify).
(e) Rs 10,000 for 1 year at 8% per annum compounded half yearly.
2. Kamala borrowed Rs 26,400 from a Bank to buy a scooter at a rate of 15% p.a. compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan? (Hint: Find A for 2 years with interest is compounded yearly and then find SI on the 2nd year amount for  years).

3. Fabina borrows Rs 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?
4. I borrowed Rs 12,000 from Jamshed at 6% per annum simple interest for 2 years. Had I borrowed this sum at 6% per annum compound interest, what extra amount would I have to pay?
5. Vasudevan invested Rs 60,000 at an interest rate of 12% per annum compounded half yearly. What amount would he get

(i) after 6 months?
(ii) after 1 year?
6. Arif took a loan of Rs 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after  years if the interest is
(i) compounded annually.
(ii) compounded half yearly.
7. Maria invested Rs 8,000 in a business. She would be paid interest at 5% per annum compounded annually. Find
(i) The amount credited against her name at the end of the second year.
(ii) The interest for the 3rd year.
8. Find the amount and the compound interest on Rs 10,000 for  years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?
9. Find the amount which Ram will get on Rs 4096, if he gave it for 18 months at  %  per annum, interest being compounded half yearly.
10. The population of a place increased to 54,000 in 2003 at a rate of 5% per annum
(i) find the population in 2001.
(ii) what would be its population in 2005?
11. In a Laboratory, the count of bacteria in a certain experiment was increasing at the rate of 2.5% per hour. Find the bacteria at the end of 2 hours if the count was initially 5, 06,000.
12. A scooter was bought at Rs 42,000. Its value depreciated at the rate of 8% per annum. Find its value after one year.