Types of Arithmetic Problems with Solutions

Important Arithmetical Verbal Reasoning Tricks

C. VENN- DIAGRAM BASED QUESTION 

Example. 1. Consider the diagram given below:

Five hundred candidate appeared in an examination comprising of tests in English, Hindi and Mathematics. The diagram gives the numbers of candidates who failed in different tests. What is the percentage of candidates who failed in at least two subjects ?

(A) 0.078

(B) 1.0

(C) 6.8

(D) 7.8

= numbers of candidates who failed in two or more subjects

= ( 10+12+12+5) = 39. $$⸫\ Required \ percentage = \left({39\over500} × 100\right)=7.8\% $$

D. Problem on ages

Example.1. Reena is twice as old as Sunita. Three years ago, she was three times as old as Sunita. How old is Reena now ?

(A) 6 years

(B) 7 years

(C) 8 years

(D) 12 years

Then, Reena’s Present age = 2x years.

Three years ago, Sunita’s age = (X-3) years and Reena’s age = (2x – 3) years.

So, (2x-3) = 3 (x-3) ↔ 2x – 3 = 3x – 9 ↔ x = 6.

⸫ Reena’s present age = 2x = 12 years.

Hence, the answer is (d)

Example.2. The age of a father is twice that of the elder son. Ten years hence the age of the father will be three times that of the younger son. If the different of ages of the two sons is 15 years, the age of the father is : 

(A) 50 years

(B) 55 years

(C) 60 years

(D) 70 years

Then, age of younger son = (x – 15) years; age of the father = 2x years.

So, 2x + 10 = 3 (x – 15 + 10) ↔ 2x + 10 = 3x – 15 ↔ x = 25.

⸫  Father’s age = 2x = 50 years. Hence, the answer is (a).

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