Maths Tricks for Problems based on Numbers Part - 1

In the previous post of Problem based on numbers we discussed about some basic concepts of this chapter. Now we will see some of the various frequently asked important question of this chapter in competition like SSC, Bank (IBPS), and Railways.

Important Types questions on Counting:-

Q1. Sum of two natural numbers is 34 and the difference between them is 20. Find the greatest natural number.

Concept:- Let two natural numbers are a & b. If the sum and difference of these numbers are given then:-

The Greatest natural number = Their (sum +difference)/2

The Smallest natural number = Their (sum - difference)/2.

Sol. Given data :- Sum = 34 and Difference = 20

The Greatest Natural Number = (sum + Difference)/ 2 = (34 + 20)/2 = 54/2 = 27.

Hence the required greatest natural number is 27.

Q2. Sum of two natural numbers is 39 and the difference between them is 11. Find the smallest natural number.

Sol. Given data :- Sum = 39 and Difference = 11

The Smallest Natural Number = (sum - Difference)/ 2 = (39 + 11)/2 = 28/2 = 14.

Hence the required smallest natural number is 14.

Q3. Sum of digits of a two- digit number is 8. If the digits of this number is reversed the number thus formed is decreased by 54. Find the two-digit number.

Concept:- Let two-digit number is (10x + y). If the sum of its digit is given then:-

x + y = given sum (first equation is formed)

When the digits of the number is reversed then the new number will be (10y + x), which increases or decreases by a given value, which is always a multiple of 9, therefore:-

x – y=[Increased by/decreased by (as given in the question)] /9. (second equation is formed)

On solving these two equation as per concept of previous question we can calculate the value of x and y, which will help us in getting two possible answers of the given question.

If it given “increases by” in the question the answer will be the smallest two-digit number.

If it given “decreases by” in the question the answer will be the greatest two-digit number.

Sol. Sum of digits of two-digit number is given therefore

x + y = 8   ....................................................... equation no.1

When the digits  are reversed the number decreases by 54, which is a multiple of 9, therefore:-

x – y = 54/9 = 6

x – y = 6   ........................................................ equation no.2

from equation 1 & 2 we get x = 7 and y = 1

Hence the possible answers might be 17 or 71.

Now as in question it is given that it “decreases by” therefore the answer will be 71.

The required two-digit number will be = 71.

Hope you have enjoyed the base concept of these types of questions this chapter till now. More Conceptual enjoyment with the Various Questions related to this chapter which are frequently asked in the examinations will be presented to your for self study on this blog soon, just keep visiting this blog regularly and writing me your related queries through comment or forum. Best of Luck for Exams. To be continued soon........................