# Notes on Quantitative Aptitude: Very Important for Competitive Exams.

As we all know how Quantitative Aptitude is very difficult and important topic from competitive exams point of view. Let us first discuss what is the meaning of quantitative aptitude? and why it is needed?

Quantitative Aptitude is a topic that every competitive exams have. It consists of questions like arithmetic reasoning, graph, percentage, ratio and proportion and problems on ages.

Quantitative Aptitude is a time bound test and therefore the candidates are tested with logical thinking and how the candidates can make effective decisions quickly under pressure. Now let us discuss the topics that you will get in your Quantitative Aptitude test.

**Percentage:-**

**Concept of Percentage:-** By a certain percent, we mean that many hundredths. Thus x percent means x hundredth, written as x%. If we want x% as a fraction:

then we have x% = x/100

Thus 20% = 20/100 , 48% = 48/100

Thus, 1/4 = ( 1/4 x 100 )% = 25%

1/2 = ( 1/2 x 100 )% = 50%

0.9 = ( 0.9 x 100 )% = 90%

If a certain value p increases by x% then increased value = ( 100 + x )% of p.

If a certain value p increases by x% then increased value = ( 100 – x )% of p.

**Questions-**

1. 5 kg of metal A and 20 kg of metal B are mixed to form an alloy. The percentage of metal A in the alloy is

a. 20% b. 25% c. 40% d.None of the these

2. An interval of 3 hours 40 minutes is wrongly estimated as 3 hours 45.5 minutes. The error percentage is

a. 2.5 b. 5 c. 5.2 d. 5.5

3. What percentage is 1 minute and 12 seconds of an hour?

a. 2% b. 10% c. 12% d. 20%

4. What percentage of 7.2 kg in 18 gms ?

a. .025% b. .25% c. 2.5% d. 25%

5. 125% of 3060 – 85% of ? = 408

a. 175 b. 180 c. 350 d. 360 e. None of these

**Profit and Loss:-**

**Concept of Profit and Loss:-**

Cost price:- The price at which an article is purchased is called as Cost Price.

Selling price:- The Price at which an article is sold is called as Selling Price.

Profit:- If the selling price is greater than cost price the seller is said to have a Profit.

Loss:- If the cost price is grater than the selling price the seller is said to have a loss.

Profit = ( S.P.) – ( C.P.)

Loss = (C.P.) – (S.P.)

Profit% = (Profit x 100/C.P.) Loss = (Loss x 100/C.P.)

S.P. = ( 100 + Gain%)/100 x C.P. S.P. = ( 100 – loss%)/100 x C.P.

C.P. = 100/( 100 + Gain%) x S.P. C.P. = 100/( 100 – loss%) x S.P.

**Questions:- **

1. If an article is sold at 200% profit, then the ratio of its cost price to its selling price will be

a. 1:2 b. 2:1 c. 1:3 d. 3:1

2. If the ratio of cost price and selling price of an article be 10:11, the percentage of profit is

a. 8 b. 10 c. 11 d. 15

3. By selling an article at some price, a man gains 10%. If the article is sold at twice of the price, the gain percentage will be

a. 20% b. 60% c. 100% d. 120%

4. The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is

a. 15 b. 16 c. 18 d. 25

5. The vendor loses the selling price of 4 oranges on selling 36 oranges. His loss percent is

a. 10% b. 11% c. 12.5% d. None of these

**Ratio and Proportion:-**

**Concept:-**

Ratio:- The Ratio of two quantities a and b in the same units, is a fraction a/b and we write it as a:b. In this a:b we call a as first term or antecedent and b as second or consequent.

Eg: 5:9 is represented as 5:9 with antecedent as 5 and consequent as 9.

Proportion:- The equality of two ratios is called Proportion.

If a:b = c:d then a:b::c:d and then we can say that a,b,c,d are in proportion.

Here a and d are called as extremes while b and c are called as mean terms

therefore product of mean = product of extremes.

Variation: We say that x is directly proportional to y, if x = ky for some constant k and we write, x proportional to y.

We say that x is inversely proportional to y, if xy = k for some constant k and we write, x proportional to 1/y.

Comparison of ratio

when we say ( a:b ) > ( c:d ) = a/b > c/d

Compounded ratio

The compounded ratio of ratios ( a:b ), ( c:d ), ( e:f ) is ( ace : bdf )

**Questions:-**

1. Which of the following is the lowest ratio?

a. 7:15 b. 15:23 c. 17:25 d. 21:39

2. If 5:a : : 20:28, then a is equal to

a. 4 b. 6 c. 7 d. 8

3. What will be the simplest form of the ratio 3 hours:1 day?

a. 1:3 b. 1:6 c. 1:8 d. 1:25

4. If 5a + 3b : 2a – 3b = 23 : 5, then the value of a:b is

a. 1:2 b. 1:4 c. 2:1 d. 4:1

In the next article I will try to come up with some new topics and questions try to solve these questions which will boost your confidence. If you like this article then please do share with your friends who are appearing for competitive exams. Do follow this site for more information and notes. Thank you. All the best.