CGL MAINS SCORE BOOSTER QUANT QUIZ-11

$A, B$ and $C$ can do a work in 37,74 and 111 days respectively. $A$ and $B$ started working together and after some days $A$ left the work and $C$ joined. Thereafter $B$ and $C$ worked for $\frac{2}{3}$ of the number of days for which $A$ and $B$ had worked together, and the work is finished what is the total number of days taken to finish the work?

Find the value of $\tan 225^{\circ} \cot 405^{\circ}+\tan$ $765^{\circ} \cot 675^{\circ}$

Three years ago, the ratio of the age (in years) of A to that of B is $4: 5$, 6 years hence, the ratio of will be $7: 8$. What will be the sum of their ages 12 years from now?

A shopkeeper marks his goods at $40 \%$ above their cost price. He is able to sell $\frac{3}{4}$ th of his goods at this price, and the remaining at $40 \%$ discount. Assuming that the shopkeeper is able to sell all the goods he buys, find his loss or gain $\%$ on the whole transaction.

The radius of cylinder is increased by $150 \%$ and its height is decreased by $20 \%$. What is percentage increased in its volume?

If $x^{2}+y^{2}+z^{2}+2=2(y-x)$, then value of: $x^{3}+y^{3}+z^{3}$ is equal to:

The value of $\frac{\sin 39^{\circ}}{\cos 51^{\circ}}+2 \tan 11^{\circ} \tan 31^{\circ} \tan 45^{\circ} \tan 59^{\circ} \tan 79^{\circ}-$ $3\left(\sin ^{2} 21^{\circ}+\sin ^{2} 69^{\circ}\right)$ is:

If the number 9765xy is divisible by both 5 and 8, then the smallest possible value of (x+ y) is:

Three pipes A, B and C are connected to a tank. A and B together can fill the tank in 30 minutes B and C together in 20 minutes and C and A together in 15 minutes. In how much time each pipe will fill the tank.

Shivani walks $9 \mathrm{~km}$ at a speed of $1 \frac{1}{2} \mathrm{~km} / \mathrm{h}$, runs $12 \mathrm{~km}$ at a speed of $3 \mathrm{~km} / \mathrm{h}$ and goes by car another $39 \mathrm{~km}$ at a speed of $13 \mathrm{~km} /$ h. If the speed of the car is considered as the speed of the Shivani. Find the average of speed of the Shivani.