Embibe Experts Solutions for Chapter: Fundamentals of Mathematics, Exercise 2: Exercise

$A$ and $B$ can do a job in $12$ days; $B$ and $C$ can do it in $16$ days. After $A$ has worked for $5$ days and $B$ has worked for $7$ days, $C$ can finish the rest in $13$ days. In how many days can $C$ do the work alone?

$A$ is thrice as efficient as $B,$ and $B$ is twice as efficient as $C\mathit{.}$ If $A, B$ and $C$ work together, how long will they take to complete a job which $B$ completes in $10$ days?

$A$ works twice as fast as $B.$ If $B$ can complete a work in $12$ days independently, then the number of days in which $A$ and $B$ can together finish the work is:

A thief escaped from police custody. Since he was sprinter he could clock $40 \frac{\mathrm{km}}{\mathrm{hr}}.$ The police realized it after $3 \mathrm{hr}.$ and started chasing him in the same direction at $50 \frac{\mathrm{km}}{\mathrm{hr}}.$ The police had a dog which could run at $60 \frac{\mathrm{km}}{\mathrm{hr}}.$ The dog could run to the thief and then return to the police and then would turn back towards the thief. It kept on doing so till the police caught the thief. Find the total distance travelled by the dog in the direction of the thief.

A cube is half-submerged inside a cubical tank filled with water. The side ratio of the cube to the tank is $1: 2$. The cube is now pressed, so that the water level rises up by $10\%$ of the dimension of the cube. How much part of the cube is left unsubmerged.

In parallelogram $ABCD$, a point $P$ is taken on $AD$ such that $AP:AD$ is $1:n$. If $BP$ intersects $AC$ at $Q$ then $AQ:AC$ is

In a parallelogram $ABCD$, $A$ point $K$ is taken on diagonal $BD$. When $AK$ is extended it intersects $CD$ and $BC$ at $M$ and $L$, respectively. If $AK=6$ units, $MK=4$ units, then$LM$ equals

There is a pyramid on a base which is a regular hexagon of side $2a$ units. If every slant edge of this pyramid is of length $\left(\frac{5a}{2}\right)$ units, then the volume of pyramid must be