Arithmetical reasoning contains calculation with special sense of reasoning. This reasoning chapter normally contains all the chapters from quantitative aptitude. So, it is one of the most interesting chapters in reasoning, because it contains both aptitude and reasoning. Arithmetic reasoning may contain the following chapters of aptitude −
- Time and work
- Time, speed, and distance
- Simple interest
- Compound interest
- Percentage
- Profit and loss
- Number system
- Average
- Ratio and proportion
Let’s explain a little bit of each type arithmetic reasoning under this heading −
Time and work − Problems on time and work will be of normal men work and men women work type problems. In such type of questions, we have to bring the number to 1 always. If it is given that 5 men can do a certain work in 10 days, and after this data it is mentioned that 10 men can take how many days to do the work then at first we have to find that, 1 man can do the job in how many days and then we can proceed further.
Time speed and distance − For problems regarding this chapter, there is one formula which we can use in this context i.e. distance = time x speed.
Simple interest − If P is taken as principal, R is taken as rate of interest, T is taken as time, and I is taken as interest then the relationship between them is
I = (P x T x R) / 100
Compound Interest − If P is principal, R is rate, amount is A and time is n years then if interest is −
Compounded annually : A = P (1 + R/100)n
Compounded half yearly : A = P [1 + (R/2)/100]2n
Compounded quarterly : A = P [1+(R/4)/100]4n
Percentage − If it is mentioned that at a certain percent, it will be meant that many hundredths. Thus if we say a percent it means a hundredths, and will be written as a %.
Profit and loss − Profit = sale price – cost price and %profit = (profit x 100) / cost price
Average − The average is a measure of central point of a set of numbers. It is an estimation of where the centre point or weight of a set of number lies.
$Average = \frac{Sum \: of \: sets \: of \: N \: numbers}{N}$
$Weighted \: average = \frac{Sum \: of \: observations \times \: weight}{Sum \: of \: weights}$
Number system − It is very important in arithmetical reasoning to know about the numbers. It is considered as backbone of mathematics.
- Natural Numbers − Natural numbers are called as counting numbers and are represented as 1, 2 , 3, 4, 5, 6,…
- Whole Numbers − Whole numbers are those numbers which start from 0 to infinity. i.e. 0, 1, 2 …0 is not a natural number.
- Integers − If we connect positive numbers and negative numbers with zero then we got integers. Also we can define integers as negative numbers + whole numbers. i.e. {..., - 3, - 2, - 1, 0, 1, 2, 3, …}
There are also even numbers and odd numbers. An even number is that number which can be divided by 2 and an odd number is that number which cannot be divided by 2.
A prime number is that number which can be divided by only two numbers that is 1 and the number itself. The smallest prime number is 2. Other prime numbers under 50 are, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47.
1 - Govt. has decided to connect Tripura and Delhi via a train service which is called ‘Tripura Sundari Express’ Two trains are running from Tripura and Delhi towards each other. Train from Tripura in covering a distance of 60 km takes 2 hours more than that of the train from Delhi. If Tripura train doubles its speed, then it would take 1 hour less than that of Delhi. Tripura train’s speed is?
Options −
A - 5
B - 10
C - 7
D - 8
Answer − Option B
Explanation − Let Tripura train's speed be X km/hr.
Then, 60/x - 60/2x = 3
6x = 60
x = 10 km/hr.
2 - Creative constructors has hired some workers from Bihar. From those newly appointed workers if 10 men working 6 hours a day can do a work in 20 days. Then 8 men working 10 hours a day can do it in how many days?
Options −
A - 15
B - 14
C - 17
D - 18
Answer − Option A
Explanation − 10 men work for 6 hours so total 60 hours and work is done in 20 days. 8 men working 10 hours means total 80 hours and the work will be completed in = (60 x 20)/80 = 15 days.
3 - Riyaz and Saqlain are two workers and they work for GPR pumps and pipes. Riyaz is twice as good a workman as Saqlain and together Riyaz and Saqlain finish a piece of work in 20 days. In how many days will Riyaz alone finish the work?
Options −
A - 90
B - 66
C - 30
D - 29
Answer − Option C
Explanation − If Riyaz takes x days to do a work then Saqlain takes 2x days to do the same work.
1/x + 1/2x = 1/20
3/2x = 1/20
x = 30 days
Hence, Riyaz alone can finish the work in 30 days.
Q 1 − A train can cover a distance of 180 km in 5 hours. What is the speed of the train? Mention it in m/s.
Options :
Answer - C
Explanation
Speed of the train is 180/5 = 36 kmph. 36 × 5/18 = 10 m/s.
Q 2 − P and Q can finish a work in 15 & 10 days. Q starts the work and leaves it after 5 days .The number of days in which P can complete the work is
Options :
Answer - C
Explanation
Q ‘s 1 day work = 1/10
Q worked for 5 days
Q 5 day work = 5/10 = 1/2
Remaining work = 1 - 1/2 = 1/2
Let P complete the remaining work in x days,
x/15 = 1/2
x = 7 1/2
Q 3 − P is thrice as good workman as Q and is therefore able to finish the work in 60 days less than Q. Q can finish the work in
Options :
Answer - C
Explanation
Let Q takes = x days
P takes = (x-60) days
Q 5 day work = 5/10 = 1/2
Work done by P in 1 day = work done by Q in 1 day
1/x-60 = 3/x, solving it
x = 90
Q 4 − Average of 5 terms is 10. Average of first two terms is 7, and last two terms is 13? What is the value of third term?
Options :
Answer - C
Explanation
Total of 5 terms = 10 × 5 = 50
Total of first two terms = 2 × 7 = 14
Total of last two terms = 13 × 2 = 26
Third term = 50 - (14 + 26) = 10
Q 5 − A bag contain Rs 150 paisa and 25 paisa coins in the ratio 8:9:11. If the total money in the bag is Rs. 366. Find the number of Rs 25 paisa coins?
Options :
Answer - C
Explanation
Let number of coins of each denomination be x.
Then 1 × 8x + ½ × 9x + 1/4 × 11x = 366 61 x/4 = 366 = x = 24.
Hence, 25 paisa coins = 11x = 11 x 24 = 264.
Q 6 − Total weight of A & B is 120 kg. If A weights 30 kg more than B? What is ratio of B: A?
Options :
Answer - B
Explanation
Let B weight = x then
A weight = x + 30, then
Total weight = x + x + 30 = 2x + 30 = 120kg x = 45. Hence, B weight = 45, A = 75
So ratio = 3:5 = 0.6
Q 7 − The average age 6 students is 17.5 years. When one student left the class, average age becomes 16 years. What is age of the student who left?
Options :
Answer - B
Explanation
Total age of 6 students = 17.5 × 6 = 105
After one left. Total age of 5 students = 5 × 16 = 80
Left student age = 105 - 80 = 25 years
Q 8 − Rs. 41517 is distributed among A,B, and C in the ratio of 3:7:11? What is B’s share?
Options :
Answer - C
Explanation
B share = 41517 × 7/21 = 1508
Q 9 − 12 year old A is three times as old as his brother B. What should be A’s age to be twice as that of B?
Options :
Answer - A
Explanation
A's present age = 12 years, B's present age = 4 years. Let A be twice as old as B after x years from now. Then, 12 = 2 (4 + x) 12 + x = 8 + 2x x = 4.
Hence, A's required age = 12 + x = 16 years
Q 10 − The addition of ages of Ramesh and Bighnesh is 45 years 4 years ago. What will be the summation of their ages 6 years hence?
Options :
Answer - C
Explanation
The summation of ages will be 45 + 10 + 10 = 65. Hence, option C.
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