The level of AFCAT exam comes with optimum difficulty. Most of the times, the questions are easy, tactical and makes the candidate take the time to solve. The questions are a bit simple than defense exams conducted by the UPSC (NDA, CDS) due to limited topics and low level of the difficulty. But, to score more you need to do good in the mathematics. So, here are 11 types of questions that are asked in the AFCAT exam and candidates should prepare them in order to score well.

### 11 Types of Maths Questions In AFCAT

**1. Simple Interest** – the questions asked related to simple interest can be different, but some direct asked questions are asked many times, where you are given few things and you have to find the missing one.

**Example** – The amount doubles at a certain rate in 5 years. In how much time will it become 8 times of the principal?

**Sol. **– If amount becomes double in 5 years, then it will become 8 times in

P = (PXRX5)/100 the R = 1/5

Now 7P = [PX(1/5)XT] / 100

= 35 years.

**2. Percentage** – the questions related to the comparison of the percentage are commonly asked in the exam.

**Example **– A’s salary is less than B by 20 percent. By what percent is B’s salary more than A?

**Sol **– Let the salary of B = 100 then A’s salary would be 80.

Now taking the percentage of B with respect to A, we get

(100/80) X100 = 125

So B’s salary is more than A by 25%

**3. Ratio** = The duplicates, triplicates sub-duplicates are very important from AFCAT point of view.

**Example** – The duplicate ratio of 5:6 is

**Sol **– The duplicate ratio of 5:6 is 5^{2}: 6^{2}

Similarly triplicates = cube of ratio

Sub-duplicates = square root of ratio.

**4. Compound interest** – the question asked can be over a given time compounded semi-annually or quarter annually. In these questions, divide the rate by 2(semi-annually) or 4(quarter annually) and multiply time by 2(semi-annually) or 4(quarter annually).

**Example **– what would be the interest on 4000 at a 10 % rate for 2 years compounded semi-annually?

**Sol. **using the formula of compound interest

Principal** –** 4000; rate = 10/2 = 5; time = 2X2 = 4

Amount. – 4000(1+5/100)^{4}

** ->** 4000(21/20)^{4}

= 4862.025

CI = 4862.025 – 4000 = 862.025

**5. Profit and loss** – these days, simply formula based questions are rarely asked on this topic. A combination of profit and loss is usually asked in AFCAT.

**Example** – A man sold an article at 5 % profit instead of selling at a loss of 5%, so she got 20 Rs more. The cost price of the article was?

**Sol. **Profit + loss = Rs. 20

5%+5% = Rs. 20

If 10% = 20 than 100% would be = (20X100) /10 = Rs.200

CP = Rs. 200

**6. Average** – Questions related to the average of a specific range of number are usually asked.

**Example 1** – The average of the first 50 even numbers are

Sol. formula – (last number + 2)/2

= 2,4,6,8,……..100

= (100+2)/2

= 102/2 = 51

**Example 2** = the average of first 50 odd numbers is

Sol. formula – (last number + 1)/2

= 1.3.5.7… 99

= (99+1)/2

= 100/2 = 50

**7. Train problems **– the problems of the train and platform are crucial and the candidates should know the basics of the questions. The problems related to the man and train and platform and train is very common.

**Example **– A man standing on the 180m long platform observes a train crossing him in 8 seconds and crossing the entire platform in 20 seconds. The speed of the train is?

**Sol** – let the length of the train be T

The speed of the train is constant. So the speed of the train while crossing the man is equal to the speed of the train while crossing the platform

T/8 = (T+180)/20

T = 120 m

Speed = 120/8 or (120+180)/20 = 15mps

15 mps X (18/5) = 54 Kmph

**8. Work and time **– Here, the questions related to the comparison of the working ability of the men, women and boy is important, which candidate must prepare. Here the candidate has to get the working compression of the type of people and then use it to solve the question.

**Example** – 8 men can complete a work in 15 days with the help of 12 boys. While 10 men can complete the same work in 18 days. In how many days, 15 boys will complete the same work?

**Sol** – (8M + 12B) X 15days = 10M X 18 Days

1M = 3B

Using this comparison, we can find

10M X 18 Days = 15 Boys X a Days

OR

30 Boys X 18 Days = 15 Boys X a Days

A = 36 Days

**9. Age** – A combination of age and ration related problems are asked in the exam which need a bit basic knowledge of both he topics to get the right answer.

**Example **– the ratio of present age of A and B is 7:5. 4 years hence, the ratio of their age will be 11:9. The present age of B is?

**Sol. **– Let the present age of A and B will be 7x and 5x.

Then their age 4 year hence would be

__7x + 4 = 11__

5x + 4 = 9

X= 1; so the present age of A and B will be 7 X 1 and 5 X 1 OR 7 and 5 years.

**10. Mensuration** – The questions related to this topic are not frequently asked, but a few questions to having a combination of percentage and dimensions are asked in the exams.

**Example** – When a towel is bleached, it was found to have lost 20% of its length and 10% of its breadth. Find the percentage of decrease in area?

**Sol.** – Let the length and breadth of the towel be 100 and 100.

Area = 10000

After reduction of length by 20% and breadth by 10%, then the new area would be = 80X90= 7200

Percentage of reduction = [10000-7200]/10000 X 100

= 28%

**11. Simplification** – The questions from simplification are usually asked by embedding a problem into a statement and the candidate has to follow the statement to get the equation.

**Example **– 7 is added to a certain number, the sum is multiplied by 5; the product is divided by 9 and 3 is subtracted from the quotient. The remainder left is 12. What is the number?

**Sol** – Let the number be x then

[__(7+x)X 5__]/9 – 3 = 12

Using BODMAS

x = 20

**Conclusion** – The type of questions asked in the AFCAT exam is wide and candidates have to practice for higher level of difficulty to get a good hold over the section. The types mentioned above are prominently observed in the AFCAT exam and candidates should prepare them perfectly. Well, mathematics is all about practice. So keep on practicing for questions as much as you can.

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