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Numbers and Ages - Aptitude Questions and Answers

This is aptitude questions and answers section on Numbers and Ages with explanation for various interview, competitive examinations and entrance tests. To make the Numbers and Ages Quiz chapter easy for you all, we are providing the basic concepts of Numbers and Ages Online Test which will surely help you to ace the test easily.

Numbers and Ages Questions - Numbers and Ages Quiz Details

Online Test Name Numbers and Ages
Exam Type Multiple Choice Questions
Category Aptitude Quiz
Number of Questions 53

Numbers and Ages Formulae

Numbers

1. (a + b)(a - b) = (a2 - b2)
2. (a + b)2 = (a2 + b2 + 2ab)
3. (a - b)2 = (a2 + b2 - 2ab)
4. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
5. (a3 + b3) = (a + b)(a2 - ab + b2)
6. (a3 - b3) = (a - b)(a2 + ab + b2)
7. (a3 + b3 + c3 - 3abc) = (a + b + c)(a2 + b2 + c2 - ab - bc - ac)
8. When a + b + c = 0, then a3 + b3 + c3 = 3abc.

Ages

1. Age after n years = X + n
2. Age n years ago = X “ n
3. n times the age = nX
4. Age of y = (Ratio of y/Sum of ratios)× sum of ages
5. Age of y = (q/p+q)× A
1. The sum of three consecutive integers is 102. Find the lowest of the three?
  • A. 40
  • B. 53
  • C. 29
  • D. 33
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Answer & Explanation

Answer: Option D

Explanation:

Three consecutive numbers can be taken as (P - 1), P, (P + 1).
So, (P - 1) + P + (P + 1) = 102
3P = 102 => P = 34.
The lowest of the three = (P - 1) = 34 - 1 = 33.

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2. The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?
  • A. 34
  • B. 28
  • C. 12
  • D. 17
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Answer & Explanation

Answer: Option B

Explanation:

Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.
P + Q = 10 ----- (1)
(10Q + P) - (10P + Q) = 54
9(Q - P) = 54
(Q - P) = 6 ----- (2)
Solve (1) and (2) P = 2 and Q = 8
The required number is = 28

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3. The sum of three consecutive even numbers is 42. Find the middle number of the three?
  • A. 14
  • B. 16
  • C. 18
  • D. 24
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Answer & Explanation

Answer: Option A

Explanation:

Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 42
6P = 42 => P = 7.
The middle number is: 2P = 14.

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4. The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?
  • A. 2/5
  • B. 7/9
  • C. 3/11
  • D. 8/5
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Answer & Explanation

Answer: Option C

Explanation:

The denominator be P, the numerator will be (P - 8).
The fraction will be (P - 8)/P.
Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.
(P - 5)/(P - 3) = 3/4
P = 20 - 9 => P = 11.
The fraction is: 3/11.

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5. The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?
  • A. 50
  • B. 60
  • C. 70
  • D. 80
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Answer & Explanation

Answer: Option C

Explanation:

A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
5 years, their ages will be 45 and 25.
Sum of their ages = 45 + 25 = 70.

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