DELHI POLICE MATHS QUIZ-59

Question 1:

If $\sin \left(3 x-20^{\circ}\right)=\cos \left(3 y+20^{\circ}\right)$, then the value of $(x+y)$ is:

$45^{\circ}$

$60^{\circ}$

$90^{\circ}$

$30^{\circ}$

Question 2:

40 liters of milk contains $10 \%$ water. How much water should be added to the mixture so that the water in the mixture becomes $20\%$?

6

10

5

8

Question 3:

By selling an article at $\frac{4}{5}$ of the marked price, there is a gain of $20 \%$. If marked price is Rs. 540 then what is the cost price of the article? (in rupees).

270

360

450

420

Question 4:

Amit and Sumit start a business together, with amit as active partner. Amit invests Rs. 3000 for 7 months and Rs. 4000 more after 7 months. Sumit invests Rs. 6000 for six month and then withdraws $50 \%$ of its initial investment for the rest of the year. Being the active partner Amit takes Rs. 250 per month as allowance, from the profit. What is the share of Sumit if the profit for the year is Rs. 15375 ?

7548

6075

7425

6225

Question 5:

Two pipes A and B can fill a tank in 12 hours and 16 hours respectively. If they are turned on alternately for one hour each starting with A, then what is the time taken (in hours) to fill the tank?

$13 \frac{4}{7}$

$13 \frac{2}{3}$

$13 \frac{3}{7}$

12

Question 6:

In given figure, a circle in cribbed in $\triangle P Q R$ with touches its side $P Q, Q R$ and $R T$ at point $S, T$ and $U$. respectively'. If $P Q=12 \mathrm{~cm}, Q R=8 \mathrm{~cm}$, and $R P=16 \mathrm{~cm}$ then find the length of $P S, Q T$ and $R U$.

$P S=10{\mathrm{cm}}, Q T=2{\mathrm{cm}}$ and RU =$8{\mathrm{cm}}$

$P S=12{\mathrm{cm}}, Q T=8{\mathrm{cm}}$ and RU= $10{\mathrm{cm}}$

$P S=10{\mathrm{cm}}, Q T=2{\mathrm{cm}}$ and RU =$6{\mathrm{cm}}$

$P S=6{\mathrm{cm}}, Q T=9{\mathrm{cm}}$ and RU =$10{\mathrm{cm}}$

Question 7:

Abha reduces her speed by $25 \%$ and so reaches home 15 minutes late. If her reduced speed is $40 \mathrm{~km} / \mathrm{hr}$, then find the distance $($ in $\mathrm{km})$ that she travelled?

40

$37 \frac{1}{2}$

50

30

Question 8:

The average age of 8 men is increased by 2 years when two of them whose age are 21 and 23 years replaced by two new men. The average age of the two new men is

22 years

24 years

28 years

30 years

Question 9:

The average score 42 students in a test is 69. The ratio of the number of boys to that of girls is $10: 11$. The average score of the boys is $20 \%$ more than that of the girls. The average score of the boys is.

72.6

70.1

72.2

75.6

Question 10:

A cuboid is of dimensions $60 \mathrm{~cm} \times 54 \mathrm{~cm} \times 30 \mathrm{~cm}$. How many small cubes with side $6 \mathrm{~cm}$ can be placed in the given cuboid?

640

630

530

450