Introduction to business mathematics chapter 1 solution aiou code 1349

Unit #1 

Business Arithmetic-1

    Solved Exercises

Q.1 Fill in the blanks . 

1. Expressing a quantitative relationship between two quantities is Ratio.
2. Ratio can reduce the quantity into lowest terms.
3. The lowest term of ratio 150:350 is   3:7.
4. Proportion can be denoted as  :: or =.
5. Two ratio are equal in proportion .
6. The external terms proportion is also known as extremes and middle term is known as means .
7. Two quantities are directly related to each other in direct proportion. 
8. 22% in the decimal is 0.22.
9. Percentage can be converted into fractional and decimal numbers.
10. 50 in percentage is 500%

Q.2 Choose the correct answer.

 1. Ratio should be reduced to ___________term.

    a)equal     b)lowest     c)highest     d)none 

2. For the quantities x,y and z the two ratios x:y and y:z are given then the ratio s:y:z is called 

    a)continued ratio     b)compound ratio     c) proportion     d)ratio 

3) Two ratio that are equal and linked by the sign of "::" or "=" are known as 

    a)ratio     b) proportion     c)both a and b     d) none 

4) simplify 20:120

    a)2:10     b) 10:20     c)2:6     d)1:6

5. Product of middle term of proportion is known as _________.

    a)product of extremes     b)product of means     c) product ratio of middle     d)both a &b

6. In direct proportion  two terms are _________.

    a)inversely     b)indirectly     c)directly     d)not 

7.Meaning of percent is __________

    a)hundredths     b)thousands     c)ten thousands     d) ten thousands .

8. Percentage is a ___________ number . 

    a)complex     b) real     c) it can be both a and b     d) none 

9. In continued proportion denominator should not be equal to __________

    a)Numerator     b)one     c)zero     d)all

10 .280 is what percent of 20000 ?

    a)1.7 %     b) 1.6%     c)1.5%     d)1.4%

Q.3 true/false 

1. In ratio the total of fractional part is always  equal to 1 . T/F
2. Ratio is denoted as :: and proportion is denoted as : . T/F
3. Ratio between 240:360 is 2:3 . T/F
4. Rate is free from the unit of measurement . T/F
5. There are three ways of presenting rate and ratio . T/F 
6. Proportion has five types . T/F
7. 2:6::y:36 where  y=12  T/F .
8. 45% of 455000 is 204750. T/F 
9. In inverse proportion if one quantity is increasing then other is also increasing . T/F
10. In compound proportion we only deal with one proportion. T/F 

Q.4 Solve the following questions . 

1. Divide Rs. 80000 in the ratio 2:6 . 

solution : 

total amount=80000

sum of the ratio =2+6=8

2/8 of total amount = 2/8 * 80000=2*10000=20000

6/8 of total amount =6/8*80000=6*10000=60000

2.Write 1/20:200 in the simplest form . 

Solution :

1/20:200/1

1*1:20*200

1:4000

3.Rs.500,000 is earned from business by the four partners. This profit is to be allocated to the four partners in the ratio 5:8:9:3 . Determine the amount of profit of each .

Solution : 

Let A,B,C and D be four partners .

Profit =5,00,000

Sum of the ratio=5+8+9+3=25 

partner A profit =5/25*5,00,000=25,00,000/25=1,00,000

partner B profit=8/25*500000=1,60,000

partner C profit =9/25*500000=1,80,000

partner D profit =3/25*500000=60,000

4. Express 58.5% to a common fraction.

Solution :

=(585/10)%

=(585/10)*(1/100)

=585/1000

=117/200

5. Solve for x in each case 4:8::x:50 and 2:40::10:x.

Solution : 

Case 1:

4:8::x:50

8*x=4*50

8x=200

x=200/8=25

6. The height of a building A is 30 feet and its shadow is 36 feet. If the height of a building B is 40 feet then how long a shadow would be ? 

Solution : 

height : shadow

30       :     36

40        :    x= ?

x/36=40/30

x=40/30 *36

  =4/3*36

  =4*12=48 feet

7.If Rs.3000 is the price of three suits of five meters in the amount of Rs. 8000 how many suits, can be purchased ? Also find the price of cloth per meter . 

let x be number of suit in Rs.8000

As  price of 3 suits = 3000

       price of 1 suit is =3000/3=1000

       x=8000/1000=8 

As   price of 5 meter suit =1000

       price of 1 meter suit =1000/5=200

8. A car runs 60 km in 5 liters of petrol. If tank is full of 20 liters, how far will it cover the distance . 

Solution : 

Speed        :    liter

60              :    5    

x=?            :    20

x/60=20/5

x/60=4

x=4*60 =240km  

9. Convert 77.87% and 24 1/5% into decimal and common fraction . 

a) 77.87%

decimal : 

=77.87%

=77.87/100

=0.7787

common fraction :

=77.87%

=(7787/100)%

=(7787/100)*(1/100)

=7787/10000

b) 24 1/5 %

= (24*5+1)/5 %

=121/5 %

Decimal : 

=121/5 %

=121/5 * 1/100

=121/500

=0.242

Common fraction : 

=121/5 % 

=121/5 * 1/100 

=121/500

10. A person spend 80 % of his/her income and saves Rs. 600. What is his/her total income ? 

let x be a total income .

saving in percentage =(100-80)%

                                  =20%

As  20% x =600

20x/100=600

20x=60000

x=60000/20

  =6000/2

x=Rs .3000

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