| Directions: In each of the following questions, a question is followed by given three statements. You have to study the question along with the statements and decide the information given in which of the statement(s) is necessary to answer the question. |
| What will be sum of two numbers? |
| I. Among the two numbers, the bigger number is greater than the smaller number by 6. |
| II. 40% of the smaller number is equal to 30% of the bigger number. |
| III. The ratio between half of the bigger number and \[\frac{1}{3}rd\] of the smaller number is 2: 1. |
A) II and III together are necessary
B) I and II together are necessary
C) Out of I, II and III any two together are necessary
D) All three, I, II and III together are necessary
E) None of the above
Correct Answer: B
Solution :
| Let the smaller number be y and larger be x. |
| I. \[x-y=6\] |
| II. \[0.4y=0.3x\]\[\Rightarrow \]\[\frac{x}{y}=\frac{4}{3}\] |
| III. \[\frac{x}{2}:\frac{y}{3}=2:1\]\[\Rightarrow \]\[\frac{x}{y}\times \frac{3}{2}=\frac{2}{1}\]\[\Rightarrow \]\[\frac{x}{y}=\frac{4}{3}\] |
| II and III give the same expression/information and hence are equivalent. |
| \[x=\frac{4}{3}y\]\[\Rightarrow \]\[x-y=6\] |
| \[\Rightarrow \] \[\frac{4}{3}y-y=6\]\[\Rightarrow \]\[\frac{y}{3}=6\] |
| \[\Rightarrow \] \[y=18\,\,\,\Rightarrow \,\,x=\frac{4}{3}\times 18=24\] |
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