In this article, we are going to discuss Business Mathematics, Business Arithmetic, Proportion, Direct Proportion, Inverse Proportion, Compound Proportion, Continued Proportion, with the help of theoretical understanding, MCQS, Short Questions, and, Extensive Questions, Solved Practice Questions,. For All Boards of Intermediate & Secondary Education paper’s preparation such as **FBISE**, **BISELHR**. **BISERWP**, **BISESARGODHA**, etc. stay connected with the **website**.

## Table of Contents

**Written by Iftikhar Ali Lecturer, Statistics, Finance and Accounting**

## Proportion, Business Arithmetic, Business Mathematics, with Solved Practice Questions, MCQS,.

## MCQS

1 | In proportion, two ratios are: | |

| (a) Equal | (b) Unequal |

| (c) One is less than other | (d) One is greater than Other |

2 | The sign of proportion is: | |

| (a) : | (b) :: |

| (c) ≠ | (d) > |

3 | Every proportion consists of: | |

| (a) One terms | (b) two terms |

| (c) three terms | (d) four terms |

4 | The middle terms of every proportion are called: | |

| (a) Central terms | (b) Extremes |

| (c) Means | (d) Upper terms |

5 | The upper and lower terms as regard to position of a proportion are called: | |

| (a) Means | (b) Extremes |

| (c) Highest & lowest terms | (d) Focal terms |

6 | The rule upholds in every proportion is: | |

| (a) Sum of means and sum of extremes are equal | (b) Difference of means and difference of extremes arc equal |

| (c) Product of means and product of extremes are equal | (d) Quotient of means and quotient of extremes are equal |

7 | In a direct proportion both the quantities concerned move in: | |

| (a) Same direction | (b) Opposite direction |

| (c) Unknown direction | (d) Known direction |

8 | In inverse proportion both the quantities move in: | |

| (a) Same direction | (b) Opposite direction |

| (c) Unknown direction | (d) Known direction |

9 | In compound proportion there exist equality of: | |

| (a) Two ratios | (b) Three ratios only |

| (c) More than two ratios | (d) Less than three ratios |

10 | The less the number of telephone calls, the lower the amount of bill, is an example of: | |

| (a) Inverse proportion | (b) Direct portion |

| (c) Compound proportion | (d) Continued proportion |

11 | If workers are to be increased to complete a job in shorter period, the quantities “workers” and “period” are: | |

| (a) Directly related | (b) Proportionally related |

| (c) Inversely related | (d) Exponentially related |

12 | | |

| (a) Direct proportion | (b) Inverse proportion |

| (c) Compound proportion | (d) Continued proportion |

13 | If 50 persons made 500 tables in 5 days. The rate of production per worker per day is: | |

| (a) 1 table | (b) 2 tables |

| (c) 3 tables | (d) 4 tables |

14 | What is the definition of a proportion in business mathematics? | |

| (a) Addition of two quantities | (b) Equality of two ratios |

| (c) Division of two numbers | (d) Subtraction of two values |

15 | In the proportion a:b=c:d, what is the antecedent? | |

| (a) a | (b) b |

| (c) c | (d) d |

16 | | |

| (a) 25 | (b) 30 |

| (c) 30 | (d) 40 |

17 | What is the cross-multiplication rule used for in proportions? | |

| (a) Finding the sum of quantities | (b) Comparing the ratios |

| (c) Solving equations | (d) Multiplying fractions |

18 | If a:b=2:3, what is the value of b if a=8? | |

| (a) 4 | (b) 6 |

| (c) 12 | (d) 9 |

19 | In the proportion 4:6=x:18, what is the value of x? | |

| (a) 10 | (b) 12 |

| (c) 9 | (d) 14 |

20 | If p:q=5:7 and q:r=2:3, what is the value of p:r? | |

| (a) 10:21 | (b) 15:21 |

| (c) 5:9 | (d) 7:10 |

21 | If 2:7 :: ?:49 is: | |

| (a) 9 | (b) 14 |

| (c) 52 | (d) 28 |

22 | Increase in men power brings decrease in task time is an example of: | |

| (a) Ratio | (b) Rate |

| (c) Proportion | (d) Fraction |

23 | What is the inverse proportion of x:y=2:6? | |

| (a) 3:2 | (b) 6:2 |

| (c) 1:3 | (d) 2:1 |

24 | If a:b=7:8 and b:c=4:5, what is a:c? | |

| (a) 14:15 | (b) 28:40 |

| (c) 7:10 | (d) 21:20 |

25 | If x:y=3:4, what is the value of y if x=15? | |

| (a) 16 | (b) 20 |

| (c) 12 | (d) 10 |

26 | In the proportion 2:5=x:15, what is the value of x? | |

| (a) 6 | (b) 4 |

| (c) 8 | (d) 10 |

27 | The expense of 40 persons for 10 days in a hotel is one million. The per day per person expense is: | |

| (a) 2000 | (b) 2500 |

| (c) 3000 | (d) 3500 |

28 | If A:B = 2:3 and B:C = 3:5. Hence A:B:C will be | |

| (a) 2:3:5 | (b) 2:5:3 |

| (c) 3:2:5 | (d) 3:5:2 |

29 | If in a problem we are given A:B :: 3:4 and B:C :: 5:7. Then it is an example of: | |

| (a) Direct Proportion | (b) Inverse proportion |

| (c) Continued Proportion | (d) Compound Proportion |

30 | Major types of proportion are: | |

| (a) One | (b) Two |

| (c) Three | (d) Four |

31 | If a, b, c, d are in direct proportion then: | |

| (a) ac=bd | (b) ab=cd |

| (c) a+b = c+d | (d) ad=bc |

32 | If a, b, c, d are in inverse proportion then: | |

| (a) | (b) |

| (c) | (d) ab=cd |

33 | If 2 kgs of fruit costs Rs. 150, 4 kgs will cost Rs. 300 is the example of: | |

| (a) Direct proportion | (b) Inverse proportion |

| (c) Compound proportion | (d) Continued proportion |

34 | If 8 person do a job in 16 days and 16 persons do a job in 8 days is an example of: | |

| (a) Direct proportion | (b) Inverse proportion |

| (c) Compound proportion | (d) Continued proportion |

35 | Using fundamental principle of proportion, what is x in 12 : x ::28 :21. | |

| (a) 12 | (b) 9 |

(c) 10 | (d) 16 |

**Short Questions**

**Define Proportion and its types with an examples**

It is a statement in Mathematics that two ratios are equal or simply we can say that it expresses the equality between two quantities in the form of:

a:b = c:d in which a and d are extremes whereas b and c are means and we can say that extremes are equal to means.

**Types of Proportion**

There are four types of Proportion discussed below:

**(1) Direct Proportion**

Direct proportion is a type of proportion in which both variables move in same direction.

**For Example**

- more men produce more output
- spending more money, you can buy more fruit

### (2) **Inverse Proportion**

Inverse proportion is a type of proportion in which either variables or quantities move in opposite directions.

**For Example**

- Employing more workers will reduce the time to complete the work.
- Using more water pumps fill the water tank earlier.

### (3) **Continued or Joint Proportion**

It is a type of proportion in which ratio of first and second quantity is equals to the ratio of third to fourth quantity and so on. It is commonly used in sharing ratio.

**For example**

Ratio between A:B = 2:3 and between B:C = 3:4 and C:D = 4:5

### (4) **Compound Proportion**

Compound proportion is a type of proportion in which more than two quantities are involved and their relation may be direct or inverse according to their nature.

**For Example**

6 men can complete the task in 4 days and produce 6 tables.

## Short Numerical Questions

**1. **Find the missing terms in each case:

**(i) 4:9::?:54 (ii) 4:30::20:?**

**Solution:**

**2.** **Mr. X saved Rs. 150.5 in 5 Days. How many days are required to save Rs. 632.1?**

**Solution:**

__Saving & Days have positive relation with each other so relation will be written as:__

**Cross Multiplication**

**3.** Find the value of x from x:250::4:50

**Solution:**

**Extensive Questions**

## Solved Practice Questions

**1:**** **If a pole of height 20 feet casts a shadow 24 feet. How long a shadow would be for a pole of height 30 feet?

**Solution:**

__Height & Shadow have positive relation with each other so relation will be written as:__

**Cross Multiplication**

**2:**** **If the price of 50 ready-made shirts is Rs. 36500 then what will be the price of 85 such shirts?

**Solution:**

__Price & shirts have positive relation with each other so relation will be written as:__

**Cross Multiplication**

**3:**** **If the price of three suits each of six meters is Rs. 2250. How many such suits can be purchased by the amount of Rs. 6750? Also find per meter price of the cloth.

**Solution:**

__Price & suits have positive relation with each other so relation will be written as:__

**Cross Multiplication**

**Per meter price:**

**One suit takes 6 meters to be sewed and 3 suits should take 18 meters whereas the price of 18-meter cloth is Rs. 2250 so the price of meter cloth should be:**

**4:**** **The distance between Lahore to Peshawar is 380 kilometers. A car runs at the speed of 45 km/hr. How much time would it take to cover the distance?

**Solution:**

**Speed Formula:**

**Distance = 380 km, Speed = 45 km/hr.**

**5: **An army formation of 900 men has a food stock for 30 days. On the same day 150 army men leave the formation. Find for how many days the same food is sufficient for the remaining army men?

**Solution:**

__If men increase, the food will be sufficient for less days so they have negative relation with each other so relation will be written as:__

**Cross Multiplication**

**6: **Some quantity of rice is sufficient for 198 persons at the rate of 1/6 kg per persons. For how many persons the same quantity of rice be sufficient if each person is to receive 1/8 kg of rice?

**Solution:**

**If quantity of rice received by each person increases, less men will be fed in given quantity so there is an inverse relation of the variables so equation will be written as:**

**Cross Multiplication**

**7:**** **A car runs 81 miles in 4.5 liters of petrol, how far will it run by a full tank of 20 liters?

**Solution:**

__If fuel increases, the miles coverage will be more so there is positive relation of the variables so equation will be written as:__

**Cross Multiplication**

**8:**** **A factory makes 560 units in 7 days with the help of 20 machines. How many units can be made in 10 days with the help of 18 machines?

__Solution:__

**Note:**

**Using more days we can produce more units so direct relation between days and units.**

**More machines will produce more units so direct relation between machine and units.**

**Now equation will be:**

**9:**** **A soap factory makes 600 units in 9 days with the help of 20 machines. How many units can be made in 12 days with the help of 18 machines?

__Solution:__

**Note:**

**Working more days, we can produce more units so direct relation between days and units.**

**More machines will produce more units so direct relation between machine and units.**

**Now equation will be:**

**10:**** **Rs. 8,000 is enough for 4 persons for 40 days. For how many days Rs. 15,000 will be enough for 5 persons? **(Lahore Board, 2007)**

__Solution:__

**Note:**

**If we have more amount, we can spend more days so there is direct relation between amount and days.**

**If we take amount constant, due to more person amount will be consumed in less days so there is inverse relation between person and days.**

**Now equation will be:**

**11:** Divide Rs. 5425 among three brothers Asghar, Mohsin & Waseem such that Asghar : Mohsin = 4:5 and Mohsin : Waseem = 9:16.

__Solution:__

**Total Amount = 5425**

**Ratio between Asghar & Mohsin = 4:5**

**Ratio between Mohsin & Waseem = 9:16**

Asghar | : | Mohsin | : | Waseem |

4 | : | 5 | | |

| | 9 | : | 16 |

36 | : | 45 | : | 80 |

**12:** Javed & Co. pays Tax of Rs. 4900. The tax is to be shared in the ratio of A : B = 3 : 5 and B : C = 5 :2. Find the tax of A, B & C.

__Solution:__

**Total Tax = 4900**

**Ratio between A & B = 3:5**

**Ratio between B & C = 5:2**

A | : | B | : | C |

3 | : | 5 | | |

| | 5 | : | 2 |

15 | : | 25 | : | 10 |

**13:**** **The three sides of a triangle are proportion 4:5:6. If the perimeter is 360 cm. Find the length of each side.

__Solution:__

**Perimeter = 360cm**

**Ratio among sides = 4:5:6**

**Sum of the ratio = 4+5+6 = 15**

**14:**** **Divide Rs. 880 in three parts so that 3 times the first, 5 times the second and 8 times the third are all mutually equal.

__Solution:__

**Total amount = 880**

**Ratio among three = 3:5:8**

**Sum of the ratio = 3+5+8 = 16**

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