Arun Sharma Solutions for Exercise 1: CAT(1999-2008, 2017)

It takes six technicians a total of ten hours to build a new server from Direct Computer, with each working at the same rate. If six technicians start to build the server at $11.00\mathrm{am}$, and one technician per hour is added beginning at $5.00\mathrm{pm}$, at what time will the server be complete?

In a coastal village, every year floods destroy exactly half of the huts. After the flood water recedes, twice the number of huts destroyed are rebuilt. The floods occurred consecutively in the last three years namely $2001,2002$ and $2003.$ If floods are again expected in $2004,$ the number of huts expected to be destroyed is:

Two straight rods $\mathrm{R}1$ and $\mathrm{R}2$ diverge from a point $\mathrm{A}$ at an angle of $120°.$ Ram starts walking from point $\mathrm{A}$ along Rlat a uniform speed of $3 \mathrm{km}/\mathrm{hr}.$ Shyam starts walking at the same time from $\mathrm{A}$ along $\mathrm{R}2$ at a uniform speed of $2 \mathrm{km}/\mathrm{h}.$ They continue walking for $4$ hours along their respective roads and reach points $\mathrm{B}$ and $\mathrm{C}$ on $\mathrm{R}1$ and $\mathrm{R}2,$ respectively. There is a straight line path connecting $\mathrm{B}$ and $\mathrm{C}.$ Then, Ram returns to point $\mathrm{A}$ after walking along the line segments $\mathrm{BC}$ and $\mathrm{CA}.$ Shyam also returns to A after walking along line segments $\mathrm{CB}$and $\mathrm{BA}.$. Their speeds remain unchanged. The time interval (in hours) between Ram's and Shyam's return to point $\mathrm{A}$ is:

If $\frac{\mathrm{a}}{\mathrm{b}}=\frac{1}{3}, \frac{\mathrm{b}}{\mathrm{c}}=2, \frac{\mathrm{c}}{\mathrm{d}}=\frac{1}{2}, \frac{\mathrm{d}}{\mathrm{e}}=3$ and $\frac{\mathrm{e}}{\mathrm{f}}=\frac{1}{4},$ then what is the value of $\mathrm{abc}/\mathrm{def} ?$ 

Ten years ago, the ages of the members of a joint family of eight people added up to $231$ years. Three years later, one member died at the age of $60$ years and a child was born during the same year. After another three years, one more member died, again at $60,$ and a child was born during the same year. The current average age of this eight member joint family is nearest to:

In Coorg, the production of tea is three times the production of coffee. If a percent more tea and b percent more coffee were produced, the aggregate amount would be $5\mathrm{c}$ percent more. But if b percent more tea and a percent more coffee were produced, the aggregate amount produced would be $3\mathrm{c}$ percent more. What is the ratio $\mathrm{a} : \mathrm{b}$?

A group of men was employed to shift $545$ crates. Every day after the first, $6$ more men than the previous day were put on the job. Also, every day after the first, each man working, shifted $5$ fewer crates than the number of crates moved by each man the previous day. The result was that during the latter part of the period, the number of crates shifted per day began to go down. $5$ days were required to finish the work. What was the number of crates shifted on the third day?

In a $10 \mathrm{km}$ race, $\mathrm{A}, \mathrm{B},$ and $\mathrm{C},$ each running at uniform speed, get the gold, silver, and bronze medals, respectively. If $\mathrm{A}$ beats $\mathrm{B}$ by $1 \mathrm{km}$ and $\mathrm{B}$ beats $\mathrm{C}$ by $1 \mathrm{km},$ then by how many metres does $\mathrm{A}$ beat $\mathrm{C} ?$