Data Sufficiency Question 44
Directions : Each of the following questions consists of a question and two statements I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and.
(BOB Junior Management
Grade/Scale-I Exam. 18.04.2015)
Mark answer (1) if the data either in statement I alone or in statement II alone are sufficient to answer the question.
Mark answer (2) if the data in both the statements I and II together are not sufficient to answer the question.
Mark answer (3) if the data in bith the statements I and II together are neccessary to answer the question.
Mark answer (4) if the data in statement I alone are sufficient to answer the question while the data in statement II alone are not sufficient to answer the question.
Mark answer (5) if the data in statement II alone are sufficient to answer the question while the data in statement I alone are not sufficient to answer the question.
- In how much time will the boat take to cover a distance of $63 km$ upstream?
I. The difference between the time taken by the boat to travel from A to B (upstream) and time taken by it to travel from $B$ to $A$ (downstream) is 2 hours.
II. The distance between $A$ and $B$ is $45 km$ and speed of the boat in still water is $12 kmph$.
Show Answer
Correct Answer: 44. (3)
Solution: 44. (3) From both statements,
If the speed of current be $x$ $\mathrm{kmph}$, then
$\frac{45}{12-x}-\frac{45}{12+x}=2$
$\Rightarrow 45\left(\frac{1}{12-x}-\frac{1}{12+x}\right)=2$
$=\frac{12+x-12+x}{(12-x)(12+x)}=\frac{2}{45}$
$\Rightarrow \frac{x}{144-x^{2}}=\frac{1}{45}$
$\Rightarrow x^{2}+45 x-144=0$
$=x^{2}+48 x-3 x-144=0$
$\Rightarrow x(x+48)-3(x+48)=0$
$\Rightarrow(x-3)(x+48)=0$
$\Rightarrow x=3 \mathrm{kmph}$
$\therefore$ Required time
$=\frac{63}{12-3}=7$ hours
BETA
