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PROBLEMS ON NUMBERS

Aptitude

PROBLEMS ON NUMBERS -> DESCRIPTION

Types of Numbers:
Natural Numbers : Counting numbers 1,2,3,4,5,..... are called natural numbers.
Whole Numbers : All counting numbers together with zero from 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.
Even Numbers : A number divisible by 2 is called an even number. e.g. 2,4,6,7,10,etc.
Odd Numbers : A number is not divisible by 2 is called an odd number. e.g. 1,3,5,6,7,9,11, etc.

PROBLEMS ON NUMBERS -> SOLVED EXAMPLES

1. 50 is divided into tow parts such that the sum of their reciprocals is 1/12 Find the two parts.
  Sol. Let the two parts be x and (50 - x)
Then, 1/x + 1/50-x = 1/12 ⇔ 50 - x + x/ x(50-x)
= 1/12 ⇒ x² - 50x + 600 = 0
⇒ (x - 30) (x - 20) = 0 ⇒ x = 30 or x = 20.
So, the parts are 30 and 20.
2. A number is as much greater than 36 as is less than 86. Find the number.
  Sol. Let the number be x. Then, x - 36 = 86 - x ⇔ 2x = 86 + 36 = 122 ⇔ x = 61.
Hence, the required number is 61.
3. Find a number such that when 15 is subtracted from 7 times the number, the result is 10 more than twice the number.
  Sol.
Let the number be x. Then, 7x - 15 = 2x + 10 ⇔ 5x = 25 ⇔ x = 5.
Hence, the required number is 5.
4. The sum of two numbers is 184. If one-third of the one exceeds one-seventh of the other by 8, find the smaller number.
  Sol.
Let the numbers be x and (184 - x). Then,
x / 3 - (184-x)/7 = 8 ⇔ 7

PROBLEMS ON NUMBERS -> Exercise

13. A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number?
 
  • A. 3
  • B. 4
  • C. 6
  • D. 8
Ans: D.
Sol.
Let the number be x.
Then, 3(2x +9) = 75
⇔ 2x + 9 = 25
⇔ 2x = 16
⇔ x = 8.
 
14. Two numbers are such that the ratio between them is 4 : 7. If each is increased by 4, the ratio becomes 3 : 5. The larger number is
 
  • A. 36
  • B. 46
  • C. 56
  • D. 64
Ans: C.
Sol.
Let the numbers be 4x and 7x.
Then, 4x+4 / 7x+4 = 3/5
⇔ 5(4x+4) = 3(7x+4)
⇔ x = 8.
∴ Larger number = 7x = 56.
 
 
15. A certain number of two digits is three times the sum of its digits and if 45 be added to it, the digits are reversed. Then number is
 
  • A. 21
  • B. 23
  • C. 27
  • D. 72
Ans: C.
Sol.
Let the ten's digit be x and unit's digit be y.
Then, 10x + y = 3(x+y) ⇒ 7x - 2y = 0
10x + y + 45 = 10y + x ⇒ y - x = 5
Solving (i) and (ii), we get : x = 2 and y = 7.
∴ Required number = 27.