DELHI POLICE MATHS QUIZ-55

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Question 1:

When operated separately, pipe A takes 5 hours less than pipe B to fill a cistern, and when both pipes are operated together, the cistern gets filled in 6 hours. In how much time (in hours) will pipe B fill the cistern, if operated separately?

Question 2:

What is the least number which when divided by 15,18 and 36 leaves the same remainder 9 in each case and is divisible by 11 ?

Question 3:

A solid lead sphere of radius 11 cm is melted and recast into small solid spheres of radius 2 cm each. How many maximum numbers (in integer) of such spheres can be made?

Question 4:

The average of twelve numbers is 39 . The average of the last five numbers is 35 , and that of the first four numbers is 40 . The fifth number is 6 less than the sixth number and 5 more than the seventh number. The average of the fifth and sixth numbers is:

Question 5:

A man brought an article and sold it at a gain of $10 \%$. If he had bought the article at $20 \%$ less and sold it for Rs. 1000 more, he would have made a profit of $40 \%$. The earlier selling price of the article (in Rs) is:

Question 6:

If $\operatorname{sin} 3 x=\cos \left(3 x-45^{\circ}\right), 0^{\circ}<3 x<90^{\circ}$, then $x$ is equal to

Question 7:

In $\triangle \mathrm{ABC}, \angle \mathrm{A}=66^{\circ} . \mathrm{AB}$ and $\mathrm{AC}$ are produced to points $\mathrm{D}$ and $\mathrm{E}$, respectively. If the bisectors of $\angle \mathrm{CBD}$ and angle $\angle B C E$ meet at the point $\mathrm{O}$, then $\angle B O C$ is equal to:

Question 8:

A person travels a distance of $300 \mathrm{~km}$ and then returns to the starting point. The time taken by him for the outward journey is 5 hours more than the time taken for the return journey. If he returns at a speed of 10 $\mathrm{km} / \mathrm{h}$ more than the speed of going, what is the average speed (in $\mathrm{km} / \mathrm{h}$ ) for the entire journey?

Question 9:

If A's salary is $60 \%$ more than B's salary, then by what percentage is B's salary less than that of $A$ ?

Question 10:

The smallest number which when divided by 12,10 and 11 leave remainders 11,9 and 10 , respectively, is: