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Top Ten Important Formulas and Problems For AFCAT Exam Preparation
We recommend you to go through the below given formulas that we have prepared. Remember them with your heart and mind, it is very necessary that you score good marks in numerical ability section of AFCAT.
1) Simplification:
- Rule of ‘BODMAS’: This BODMAS rule depicts the correct sequence in which the operations are to be executed, so as to find out the value of given expression. Full form of BODMAS is B – Bracket, O – of, D – Division, M – Multiplication, A – Addition and S – Subtraction. Thus, while solving or simplifying a problem, first remove all brackets, strictly in the order (), {} and ||. After removing the brackets, we will use the following operations strictly in the following order: (i) of (ii) Division (iii) Multiplication (iv) Addition (v) Subtraction.
2) Average:
- Average = (Sum of observations/Number of observations)
- Suppose a train covers a certain distance at x kmph and an equal distance at y kmph. Then, the average speed of train during the whole journey is kmph (2xy/x+y)kmph.
3) Percentage:
- By a certain percent, we mean that many hundredths. Thus, x percent means x hundredths, written as x%. To express x% as a fraction: We have, x% = x/100
- To express a/b as a percent: We have, a/b = (a/b x 100)%
- Percentage Increase/Decrease: If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is: [(R/(100+R)) x 100]%. If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is: [(R/(100-R)) x 100]%.
- Result on Population: Let the population of a town be P now and suppose it increases at the rate of R% per annum, then: population after n years = P (1+(R/100))n Population n years ago= P/ (1+(R/100))n
- Result on Depreciation: Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then: Value of the machine after n years = P (1-(R/100)n , Value of the machine n years ago = P/ (1-(R/100)n, If A is R% more than B, then B is less than A by [(R/(100+R)) x 100] %, If A is R% less than B, then B is more than A by [(R/(100-R)) x 100] %
4) Ratio:
- Rule: The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio. Eg. 4 : 5 = 8 : 10 = 12 : 15. Also, 4 : 6 = 2 : 3.
5) Proportion:
- The equality of two ratios is called proportion. If a : b = c : d, we write a : b :: c : d and we say that a, b, c, d are in proportion. Here a and d are called extremes, while b and c are called mean terms. Product of means = Product of extremes. Thus, a : b :: c : d (b x c) = (a x d).
6) Simple Interest:
- Principal: The money borrowed or lent out for a certain period is called the principal or the sum.
- Interest: Extra money paid for using other’s money is called interest.
- Simple Interest (S.I.): If the interest on a sum borrowed for certain period is reckoned uniformly, then it is called simple interest. Let Principal = P, Rate = R% per annum (p.a.) and Time = T years. Then Simple Interest = (P x R x T)/100
7) Profit and Loss:
- Cost Price: The price, at which an article is purchased, is called its cost price, abbreviated as C.P.
- Selling Price: The price, at which an article is sold, is called its selling prices, abbreviated as S.P.
- Profit or Gain: If S.P. is greater than C.P., the seller is said to have a profit or gain.
- Loss: If S.P. is less than C.P., the seller is said to have incurred a loss.
- Gain = (S.P.) – (C.P.)
- Loss = (C.P.) – (S.P.)
8) Decimal Fraction:
- A decimal fraction is a fraction in which denominator is an integer power of ten. (The term decimals are commonly used to refer decimal fractions). Generally, a decimal fraction is expressed using decimal notation and its denominator is not mentioned explicitly
Examples: 1/10 = .1 , 1/100 = .01
- Conversion of a Decimal into Common Fraction: Put 1 in the denominator under the decimal point and annex with it as many zeros as is the number of digits after the decimal point. Now, remove the decimal point and reduce the fraction to its lowest terms.
9) Compound interest formula
The formula for annual compound interest is A = P (1 + r/n) ^ nt:
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for
10) Arithmetic Series formula
In an Arithmetic Sequence the difference between one term and the next is a constant.
say: {a, a+d, a+2d, a+3d, … }
We can write an Arithmetic Sequence as a rule:
xn = a + d(n-1)
(We use “n-1” because d is not used in the 1st term).
AFCAT EXAM PROBLEMS
1. Anmol sold 2 items for rupees 1000 each. On one, he gained 10% and on other he lost 10%. How much did a gain or lost in the whole
transaction?
a. Profit 0.95 %
b. Loss 1%
c. Profit 10%
d. Loss 10%
2. The price of an item is decreased by 25%. What percent increase must be done in new price to get the original price?
a. 33 â…“%
b. 43 ¾ %
c. 55 â…”%
d. 65 ¼%
3. A’s Salary is 50% more than B’s. How much percent is B’s Salary less than A’s?
a. 63 ¼%
b. 43 ¼%
c. 53 â…“%
d. 33 â…“ %
4. In Arun’s opinion, his weight is greater than 65 kgs but less than 72 kgs. His brother does not agree with Arun and he is things that Arun weight is greater than 60 kgs but less than 70 kg. His mother’s view is that hIs weight can’t be greater than 68 kgs. If all of them are correct and their estimation, what is the average of different probable rates of Arun?
a. 67 kgs
b. 68 kgs
c. 69 kgs
d. Data Inadequate
5. A train 150 metres long is running with a speed of 68 kmph. And what time will it pass a man who is running at 8 kilometres per hour in the same
direction in which the train is going.
a. 8 seconds
b. 8.5 seconds
c. 9 seconds
d. 9.5 seconds
6. a and b can do a piece of work and 30 days while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10
days when B and C leave. How many days more will A take to finish the work?
a. 18 days
b. 24 days
c. 30 days
d. 36 days
7. A sum was invested for 3 years at simple interest at a certain rate. Had it been invested at 4% higher rate of interest, it would have fetched 600 more. The sun is
a. Rupees 4000
b. Rupees 4950
c. Rupees 5000
d. Rupees 5150
8. The difference between simple and compound interest compounded annually on a certain sum of money for 2 years at 4% per annum is Rupee 1. The sun is
a. 625
b. 630
c. 640
d. 650
9. A man rows to a place 48 kilometres distance and come back in 14 hours. He finds that he can Row 4 kilometre with the stream in the same time as three kilometres against the stream. The rate of stream is
a. 1 kilometre per hour
b. 1.5 kilometre per hour
c. 2 kilometre per hour
d. 2.5 kilometre per hour
10. Income of Ram and Shyam are in the ratio of 3:4 and their expenditures and the ratio of 4:5, find the ratio of their savings, given that shyam saves third of his income.
a. 10: 15
b. 13:20
c. 15:20
d. 13:15
