Arun Sharma Solutions for Exercise 3: XAT(2008-17)

City Bus Corporation runs two buses from terminus $\mathrm{A}$ to terminus $\mathrm{B},$ each bus making $5$ round trips in a day. There are no stops in between. These buses ply back and forth on the same route at different but uniform speeds. Each morning the buses start at $7 \mathrm{AM}$ from the respective terminuses. They meet for the first time at a distance of $7 \mathrm{km}$ from terminus $\mathrm{A}.$ Their next meeting is at a distance of $4 \mathrm{km}$ from terminus $\mathrm{B},$ while travelling in opposite directions. Assuming that the time taken by the buses at the terminuses is negligibly small, and the cost of running a bus is $₹20$ per $\mathrm{km}$, find the daily cost of running the buses (in $₹$).

Ram and Shyam form a partnership (with Shyam as working partner) and start a business by Investing $₹4000$ and $₹6000$ respectively. The conditions of partnership were as foIIows:

In case of profits till $₹200,000$ per annum, profits would be shared in the ratio of the invested capital.

Profits from $₹200,001$ till $₹400,000$ Shyam would take $20\%$ out of the profit, before the division of remaining profits, which will then be based on ratio of invested capital.
Profits in excess of $₹400,000,$ Shyam would take $35\%$ out of the profits beyond $\mathrm{Rs} 400,000,$ before the division of remaining profits, which will then be based on ratio of invested capital.

If Shyam's share in a particular year was $₹367000,$ which option indicates the total business profit (in $₹$) for that year?

Prof. Mandal walks to the market and comes back in an auto. It takes him $90$ minutes to make the round trip. If he takes an auto both ways it takes him $30$ minutes. On Sunday, he decides to walk both ways. How long would it take him?

Mr. Mehra is planning for higher education expenses of his two sons aged $15$ and $12$. He plans to divide $₹15$ lacs in two equal parts and invest in two different plans such that his sons may have access to $₹21$ lacs each when they reach the age of $21.$ He is looking for plan that will give him a simple interest per annum. The rates of interest of the plans for his younger son and elder son should be

The tax rates for various income slabs are given below.

There are $15$ persons working in an organization. Out of them, $3$ to $5$ persons are falling in each of the income slabs mentioned above. Which of the following is the correct tax range of the $15$ persons? (E.g. If one is earning $₹2000,$ the tax would be: $500\times 0+1500\times 0.05)$

Devanand's house is $50 \mathrm{km}$ West of Pradeep's house. On Sunday morning, at $10 \mathrm{a}.\mathrm{m}.,$ they leave their respective houses. Under which of the following scenarios, the minimum distance between the two would be $40 \mathrm{km}?$
Scenario $\mathrm{I}:$ Devanand walks East at a constant speed of $3 \mathrm{km}$ per hour and Pradeep walks South at a constant speed of $4 \mathrm{km}$ per hour.
Scenario $\mathrm{II}:$ Devanand walks South at a constant speed of $3 \mathrm{km}$ per hour and Pradeep walks East at a constant speed of $4 \mathrm{km}$ per hour.
Scenario $\mathrm{III}:$ Devanand walks West at a constant speed of $4 \mathrm{km}$ per hour and Pradeep walks East at a constant speed of $3 \mathrm{km}$ per hour.

The median of $11$ different positive integers is $15$ and seven of those $11$ integers are $8,12,20,6,14,22,$ and $13 .$

Statement $\mathrm{I}:$ The difference between the averages of four largest integers and four smallest integers is $13.25.$

Statement $\mathrm{II}:$ The average of all the $11$ integers is $16 .$

Which of the following statements would be sufficient to find the largest possible integer of these numbers?

Three pipes are connected to an inverted cone, with its base at the top. Two inlet pipes, $\mathrm{A}$ and $\mathrm{B},$ are connected to the top of the cone and can fill the empty cone in $8$ hours and $12$ hours, respectively. The outlet pipe $\mathrm{C},$ connected to the bottom, can empty a filled cone in $4$ hours. When the cone is completely filled with water, all three pipes are opened. Two of the three pipes remain open for 20 hours continuously and the third pipe remains open for a lesser time. As a result, the height of the water inside the cone comes down to $50\%.$ Which of the following options would be possible?