The question given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is/are sufficient to answer the given question. Read the both statements and give answer
What is the sum of two numbers ?
I. The bigger of these two numbers is 6 more than the smaller number
II. 40% of the smaller number is equal to 30% of the bigger number
III. The ratio between half of the bigger number and one - third of the smaller number is 2 : 1

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II and III are sufficient

I and II are sufficient

I and either II or III is sufficient

All I, II and III together are sufficient

answer is C.

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Detailed Solution

Solution: Let the two numbers be x and y such that x < y

Given:

$\begin{array}{l} I) y = x + 6 \to (1) \\ I I) 40 % o f x = 30 % o f y \\ I) \frac{40}{100} \times x = \frac{30}{100} \times y \\ 0.4 x - 0.3 y \\ I I) 40 % o f x = 30 % o f y \\ \frac{40}{100} \times x = \frac{30}{100} \times y \\ 0.4 x - 0.3 y \\ \frac{x}{y} = \frac{3}{4} \to (2) \\ L e s s m u l t i p l y (1) w i t h 3 \\ 3 y = 3 x + 18 \\ 4 x = 3 x + 18 \\ x = 18 \\ I I I) (\frac{1}{2} \times y) : (\frac{1}{3} \times x) = 2 : 1 \\ \Rightarrow \frac{\frac{y}{2}}{\frac{x}{3}} = \frac{2}{1} \\ \Rightarrow \frac{3 y}{2 x} = \frac{2}{1} \\ \Rightarrow \frac{y}{x} = \frac{4}{3} \Rightarrow \frac{x}{y} = \frac{3}{4} \to (3) \\ S u b' x' v a l u e i n e q u . (1) \\ y = 18 + 6 \\ y = 24 \\ ∴ S u m o f x a n d y \Rightarrow 18 + 24 = 42 \end{array}$