Numbers Aptitude Questions with Answers

1.In a 2 digit numbers, the digit in the unit’s place is 2 times the digit in 10’s place and sum of the digits is equal to 9. What is the number?

30 16 36 56

2.The difference between a 2 digit numbers & the number getting by place changing the 2 digits is 54. What is the difference between the 2 digits of that particular number?

5 6 7 8

3.The sum of the digits of a 2 number is 2/5 of the difference between the number and the number obtained by place changing the positions of the particular digits. What is the exact difference between the particular digits of the number?

5 6 Cannot be determined None of these

4.The difference between 2 numbers is 1356. When the largest number is divided by the smallest one, the quotient is 6 and the remainder is 15. The smaller number is ?

570 270 370 470

5.If the number getting on position changing the digits of a 2 digit number is 18 more than the original number and the sum of the digits is 6. What is the particular original number?

42 52 62 72

6.The product of 4 consecutive even numbers is always divisible by?

384 284 584 684

7.The sum of two positive integers multiplied by the bigger number is 204, and their difference multiplied by the smaller number is 35. What are the numbers?

12,5 13,5 14,5 16,5

8.The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. What is the sum of the numbers?

500 400 600 700

PROBLEMS ON NUMBERS -> DESCRIPTION

In this section, questions involving a set of numbers are put in the form of a puzzle. You have to analyse the given conditions, assume the unknown the numbers and form equations accordingly, which on solving yield the unknown numbers.

AVERAGE -> IMPORTANT FACTS AND FORMULAE 

I. Average = [Sum of observations / Number of observations] 

II. Suppose a man covers a certain distance at x kmph and an equal distance at y kmph. Then, the average speed during the whole journey is [2xy / x + y] kmph.

Numbers -> IMPORTANT FACTS AND FORMULAE 

1. Natural Numbers : Counting numbers 1, 2, 3, 4, 5, .. are called natural numbers. 

II. Whole Numbers : All counting numbers together with zero form the set of whole numbers. 

Thus, I. 0 is the only whole number which is not a natural number.  

II. Every natural number is a whole number. 

III.Some Important Formulae :

 I. ( 1 + 2 + 3 + .....+ n) = n (n + 1 ) / 2 

II. (1 2 + 22 + 32 + ..... + n2) = n ( n + 1 ) (2n + 1) / 6 

III. (1 3 + 23 + 33 + ..... + n3) = n2 (n + 1)2 / 4 

SIMPLE INTEREST -> IMPORTANT FORMULAE

1. Principal : The money borrowed or lent out for a certain period is called the principal of he sum.

2. Interest : Extra money paid for using other’s money is called interest. 

3. Simple Interest (S.I.) : If the interest on a sum borrowed for a 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, 

(i) S.I. = [P * R * T / 100] 

(ii) P = [100 * S.I. / R * T] 

R = [100 * S.I / P * T] and T = [100 * S.I. / P * R]  

TRUE DISCOUNT -> IMPORTANT CONCEPTS

Suppose a man has to pay Rs. 156 after 4 years and the rate of interest is 14% per annum. Clearly, Rs. 100 at 14% will amount to Rs. 156 in 4 years. So, the payment of Rs. 100 now will clear off the debt of Rs. 156 due 4 years hence.

We say that :

Sum due = Rs. 156 due 4 years hence;

Present worth (P.W.) = Rs.100; True Discount (T.D.) = Rs. (156 - 100) = Rs. 56 = (Sum due) - (P.W.). We define : T.D. = Interest on P.W. Amount = (P.W.) + (T.D.). Interest is reckoned on P.W. and true discount is reckoned on the amount.

TRUE DISCOUNT -> IMPORTANT FORMULAE 

Let rate = R% per annum and Time = T years.

Then,

I. P.W. = 100 * Amount / 100 + (R*T) = 100 * T.D. / R * T

II. T.D. = (P.W.)* R * T / 100 = Amount * R * T / 100 + (R * T)

III. Sum = (S.I.) * (T.D.) / (S.I.) - (T.D.)

IV. (S.I.) - (T.D.) = S.I on T.D. V.

When the sum is put at compound interest, then P.W. = Amount / [1+R/100]T;  

PROBLEMS ON TRAINS -> IMPORTANT FORMULAE

1. a km/hr = [a * 5/18]m/s. 

2. a m/s = [a * 18/5] km/hr. 

3. Time taken by a trian of length l metres to pass a pole or a standing man or a signal post is equal to the time taken by the train to cover l metres. 

4. Time taken by a train of length l metres to pass a stationary object of length b metres is the time taken by the train to cover (l + b) metres. 

5. Suppose two trains or two bodies are moving in the same direction at u m/s and v m/s, where u>v, then their relatives speed = (u - v) m/s. 

6. Suppose two trains or two bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (u + v) m/s 

7. If two trains of length a metres and b metres are moving in opposite directions at u 

8. If two trains of length a metres and b metres are moving in the same direciton at u m/s and v m/s, then the time taken by the faster train to cross theslower train = (a + b)/(u - v) sec. 

9. If tow trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then (A’s speed) : (B’s speed) = (√b : √a).

CLOCKS -> IMPORTANT FORMULAE

The face or dial of a watch is a circle whose circumference is divided into 60 equal parts, called minute spaces. A clock has two hands, the smaller one is called the hour hand or short hand while the larger one is called the minute hand or long hand. 

I. In 60 minutes, the minute hand gains 55 minutes on the hour hand. 

II. In every hour, both the hands coincide once. 

III. The hands are in the same straight line when they are coincident or opposite to each other. 

IV. When the two hands are at right angles, they are 15 minute spaces apart. 

V. When the hands are in opposite directions, they are are 30 minute spaces apart. 

VI. Angle traced by hour hand in 12 hrs = 360°. 

VII. Angle traced by munute hand in 60 min. = 360°

Too Fast and Too Slow : If a watch or a clock indicates 8.15, when the correct time is 8, it is said to be 15 minutes too fast. 

On the other hand, if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes too slow. 

BANKERS DISCOUNT -> IMPORTANT CONCEPTS

Bankers’ Discount : Suppose a merchant A buys goods worth, say Rs. 10,000 from another merchant B at a credit of say 5 months. Then, B prepares a bill, called the bill of exchange. A signs this bill and allows B to withdraw the amount from his bank account after exactly 5 months. 

The date exactly after 5 months is called nominally due date. Three days (known as grace days) are added to it to get a date, known as legally due date. 

Suppose B wants to have the money before the legally due date. Then he can have the money from the banker or a broker, who deducts S.I. on the face value (i.e., Rs. 10,000 in this case) for the period from the date on which the bill was discounted (i.e., paid by the banker) and the legally due date. This amount is known as Banker’s Dicount (B.D.) 

Thus, B.D. is the S.I. on the face value for the period from the date on which the bill was discounted and the legally due date. 

Banker’s Gain (B.G.) = (B.D.) - (T.D.) for the unexpired time.

Note : When the date of the bill is not given, grace days are not to be added. 

BANKERS DISCOUNT -> IMPORTANT FORMULAE

I. B.D. = S.I. on bill for unexpired time.

II. B.G. = (B.D.) - (T.D.) = S.I. on T.D. = (T.D.)² / R.W. 

III. T.D. = √P.W. * B.G. 

IV. B.D. = [Amount * Rate * Time / 100] 

V. T.D. = [Amount * Rate * Time / 100 + (Rate * Time)]

VI. Amount = [B.D. * T.D. / B.D. - T.D.] 

VII. T.D. = [B.G. * 100 / Rate * Time] 

PARTNERSHIP -> IMPORTANT FACTS AND FORMULAE

I. Partnership : When two or more than two persons run a business jointly, they are called partners and the deal is known as partnership. 

II. Ratio of Division of Gains : 

(i) When investments of all the partners are for the same time, the gain or loss is distributed among the partners in the ratio of their investments. Suppose A and B invest Rs. x and Rs. y respectively for a year in a business, then at the end of the year : (A’s share of profit) : (B’s share of profit) = x : y. 

(ii) When investments are for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital * number of units of time). Now, gain or loss is divided in the ratio of these capitals. Suppose A invests Rs. x for p months and B invests Rs. y for q months, then (A’s share of profit) : (B’s share of profit) = xp : yq. 

III. Working and Sleeping Partners : A partner who manages the business is known as working partner and the one who simply invests the money is a sleeping partner.