RK JHA Solutions for Chapter: Data Interpretation and Quantitative Ability, Exercise 5: Solved Paper 2016

The difference between the area of the circumscribed circle and the area of the inscribed circle of an equilateral triangle is $2156 \mathrm{sqcm}$. What is the area of the equilateral triangle?

A person standing on the ground at point $\mathrm{A}$ saw an object at point $\mathrm{B}$ on the ground at a distance of $600 \mathrm{m}$. The object started flying towards him at an angle of $30°$ with the ground. The person saw the object for the second time at point $\mathrm{C}$ flying at $30°$angle with him. At point $\mathrm{C}$, the object changed direction and continued flying upwards. The person saw the object for the third time when the object was directly above him. The object was flying at a constant speed of $10 \mathrm{km}/\mathrm{h}$.

Find the angle at which the object was flying after the person saw it for the second time. You may use additional statement(s) if required.

Statement I: After changing direction, the object took $3$ more minutes than it had taken before.

Statement II: After changing direction, the object travelled an additional $200\sqrt{3} \mathrm{m}$.

$\mathrm{f}$ is a function for which $\mathrm{f}\left(1\right)=1$ and $\mathrm{f}\left(\mathrm{x}\right)=2\mathrm{x}+\mathrm{f}(\mathrm{x}-1)$ for each natural number $\mathrm{x}\ge 2$. Find $\mathrm{f}\left(31\right)$.

A water tank has $\mathrm{M}$ inlet pipes and $\mathrm{N}$ outlet pipes. An inlet pipe can fill the tank in $8 \mathrm{h}$ while an outlet pipe can empty the full tank in $12 \mathrm{h}$. If all pipes are left open simultaneously, it takes $6 \mathrm{h}$ to fill the empty tank. What is the relationship between $\mathrm{M}$ and $\mathrm{N} ?$

Company $\mathrm{ABC}$starts an educational program in collaboration with Institute XYZ. As per the agreement, ABC and XYZ will share profit in $60: 40$ ratio. The initial investment of ₹$100000$ on infrastructure is borne entirely by $\mathrm{ABC}$ whereas the running cost of ₹$400$ per student is borne by $\mathrm{XYZ}$. If each student pays $₹2000$ for the program, find the minimum number of students required to make the program profitable, assuming $\mathrm{ABC}$ wants to recover its investment in the very first year and the program has no seal limits.

Study the figure below and answer the question.

Four persons walk from point $\mathrm{A}$ to point $D$ following different routes. The one following $\mathrm{ABCD}$ takes $70 \min .$ Another person takes $45 \min$ following $\mathrm{ABD}$. The third person takes $30 \min$ following route $\mathrm{ACD}$. The last person takes $65 \min$ following route $\mathrm{ACBD}$. If all were to walk at the same speed, how long will it take to go from point $\mathrm{B}$ to point $\mathrm{C} ?$

Each day on planet $\mathrm{M}$ is $10 \mathrm{h}$, each hour $60 \min$ and each minute $40 \mathrm{s}$. The inhabitants of planet $\mathrm{M}$ use $10 \mathrm{h}$ analog clock with an hour hand, a minute hand and a second hand. If one such clock shows $3 \mathrm{h}$ $42 \min$ and $20 \mathrm{s}$ in a mirror, what will be the time in planet $\mathrm{M}$ exactly after $5 \min ?$

In the figure below, two circular curves create $60°$ and $90°$ angles with their respective centres. If the length of the bottom curve $\mathrm{Y}$ is $10\pi$, find the length of the other curve.