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Question 1

Find the ratio of the following

a) Speed of a cycle 15 km per hour to the speed of scooter 30km per hour.
b) 5m to 10km
c) 50 paise to Rs. 5.


Solution:
a) Speed of a cycle 15 km per hour to the speed of scooter 30km per hour.

The ratio of the speed of a cycle to the speed of scooter = 15:30

The comparison can be done by using fractions as

In terms of ratio 1:2

b) 5m to 10km

c) 50 paise to Rs. 5.
1 Rs = 100 paise
5 Rs = 500 paise
∴ 50 paise : 500 paise The ratio is 1:10.

Question 2

Convert the following ratios to percentages.

a) 3:4
b) 2:3.

Solution:
a) 3:4

b) 2:3



Question 3

72% of 25 students are good in mathematis. How many are not good in mathematics?


Solution:
100 - 72 = 28%
28 % of 25 = students are not good in mathematics.


Question 4

A football team won 10 matches out of the total number of matches they played. If the won percentage was 40, then how many matches did they play altogether?

Solution:
Let the number of matches played in all be x.

40% of x = 10

Total matches played = 25.

Question 5

If Chameli had Rs. 600 left spending 75% of her money how much did she have in the beginning?


Solution:
Spending = 75% of her money

Let over = 25%

Let x be the money in the beginning.

Chameli had Rs. 2400 in the beginning.

Question 6

If 60% people in a city like cricket, 30% like football and the remaining like other games, then what percent of the people like other games? If the total number of people are 50 lakh. Find the exact number who like each type of game.


Solution:
Percentage of people like cricket = 60%

Percentage of people like football = 30%

Percentage of people like other game = 100 - (60 + 30) = 100 - 90 = 10%

Total number of people = 50,00,000

Number of people like cricket

Number of people like football

Number of people like other game

Question 7

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


Solution:
New Salary = 1,54,000
Increased salary = 10%
Original salary


Question 8

On Sunday 845 people went to the zoo. On Monday only 169 people went. What is the percent decrease in the people visiting the zoo on Monday.

Solution:
Number of people visited on Sunday = 845

Number of people visited on Monday = 169.

845 - 169 = 676

Decrease percent on Monday


Question 9


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:
Prize of 80 articles = Rs. 2400

Prize of one articles

Profit = 16%

Selling prize of one article

Question 10

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 prize of the article.


Solution:
The cost of an article = Rs. 15,500
Repair changes             = Rs.     450
                                       ________
                          Total = Rs. 15950
                                       ------------
Profit = 15%
Selling prize of an article


Question 11

A VCR and TV were bought for Rs. 8000 each. The shopkeeper incurred a loss of 4.1% on the VCR and a profit of 8% on the TV. Find the gain or loss percent on the whole transaction.

Solution:
Loss 4% on VCT =

Profit 8% on TV

Total CP = Rs. 8000 + Rs. 8000 = Rs. 16000

Total SP = Rs. 7680 + Rs. 8640 = Rs. 16320

Since total SP > total CP, a profit of Rs(16320 - 16000) or Rs. 320

Profit percentage

Gain 2%

Question 12

During a sale, a shop offered a discount 10% on he marked prizes of all 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:
Marked Price of jeans = Rs. 1450

Discount = 10%

Sale price = Rs(1450 - 145) = Rs. 1305

MP of Two shirts = Rs. 850 × 2 = 1700

For 1 shirt Discount = 10%

Sale price of 2 shirts = 1700 - 170 = Rs. 1530

Bill amount = Rs. 1305 + Rs. 1530 = Rs. 2835.

Question 13

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.

 


Solution:
Gain of 5% = Rs.

Loss of 10% =

P = 40000 - 39000 = Rs. 1000

Profit = Rs. 1000.

Question 14

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 it if he buys it.


Solution:
The price of a TV = Rs. 13,000
On Rs 13000, the tax

Bill amount = cost of item + sales tax
                 = Rs. 13000 + Rs. 1560
                 = Rs. 14560

The amount that vinod will have to pay it if he buys it = Rs. 14560.

Question 15

I purchased a gain dryer for Rs. 5,400 including 8% VAT. Find the price before VAT was added.


Solution:
VAT = 8%
Cost


Question 16

Calculate the amount and compound interest on Rs. 10,800 for 3 years at per annum compounded annually.

Solution:


Question 17

Calculate the amount and compound interest on Rs. 18,000 for years at 10% per annum compounded annually.

Solution:

5 half years in years, compounding to be done in 5 times.

Rate of Interest = half of 10% = 5% half yearly.

A = Rs. 22973.0681

CI = A - P = 22973.0681 - 18000 = Rs. 4973.0681.

Question 18

Calculate the amount and compound interest on Rs. 62,500 for years at 8% per annum compounded half yearly. 3 half years in years.

Solution:
Rate of interest = half of 8% = 4% half yearly.



Question 19

Calculate the amount and compound interest on Rs. 8000 for 1 year at 8% per annum compounded half yearly.


Solution:
2 half years in one year.

Rate of interest = half of 8% = 4% half yearly



Question 20

Calculate the amount and compound interest on Rs. 10000 for 1 year at 8% per annum compounded half yearly.


Solution:
2 half years in one year.

Rate of interest = half of 8% = 4% half yearly



Question 21

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?


Solution:
2 years 4 months = 2 years years r = 15%

                           

For 2 years:

For years:

For years

A = Rs. 34916 + Rs. 1745.70 = Rs. 36659.70.


Question 22

Fabina borrows Rs. 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same period at 10% per annum, compounded annually. Who pays more interest and by how much?

 


Solution:
Interest for Fabina:
For Rs. 12,500 interest charged

Interest for 3 years = 3 × 1500 = Rs. 4500

Interest for Radha:
CI for 3 years & R = 10%

Interest = Rs. 16,637.5 − 12,500 = Rs. 4137.50

Difference between the two interest = Rs. 4500 − Rs. 4137.50

Fabina pays more interest by =

Question 23

I borrowed Rs. 12,000 from Janushed 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?


Solution:
Simple Interest =

SI for 2 years = 2 × 720 = Rs. 1440

Compound Interest:

A - P = 13483.2 - 12000 = Rs. 1483.20

Extra amount = 1483.20 - 1440 = Rs. 43.20.

Question 24

Vasudevan invested Rs. 60000 at an interest rate of 12% per annum compounded half yearly. What amount would he get

(i) after 6 months (ii) after 1 year?


Solution:

(i)

After 6 months Vasudevan would get = Rs. 63,600

(ii)

After 1 year Vasudevan would get = Rs. 67,416.

Question 25

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 in (i) compounded annually (ii) compounded half yearly.


Solution:
(i) Compounded annually:

For half year

(ii) Compounded half yearly:
years = 3 half - years



Question 26

Maria invested Rs. 8000 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.


Solution:

(ii) Interest for the 3rd year

Question 27

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.


Solution:
18 months = 12 months + 6 months = 3 half years



Question 28

The population of a place increased to 54000 in 2003 at a rate of 5% per annum.

(i) Find the population in 2001 (ii) What would be its population in 2005?

Solution:
Population in 2003 = 54000

5% in 2002 =

                = 54000 - 2700 = 51300

5% in 2001 =

Population in 2001 = 51300 - 2565 = 48735

Population in 2003 = 54000

Increase 5% =

Population in 2004 = 54000 + 2700 = 56700

Increase 5% =

Population in 2005 = 56700 + 2835 = 59,535.

Question 29

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.


Solution:
Initial count = 5,06,000

At the end of 1 hr =

At the end of 1 hr = 5,06,000 + 12650 = 518650

At the end of 2nd hr =

                            = 12966.25 + 518650

At the end of 2 hours = 5,31,616.

Question 30

A scooter was bought at Rs. 42,000. Its value depreciated at the rate of 8% per annum. Find its value after one year.

 


Solution:
Reduction = 8% per annum
                 

Value after one year = Rs. 42000 - 3360 = Rs. 38,640.





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