DELHI POLICE MATHS QUIZ-29

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Question 1:

I is the incentre of $\triangle A B C,  \angle A B C=60^{\circ}$ and $\angle A C B=50^{\circ}$ then find $\angle \mathrm{BIC}$.

Question 2:

If two lines $2 x+3 y=8,4 x-\mathrm{ky}=16$ has infinite numbers of solution then find $\mathrm{k}$.

Question 3:

5 women and 2 men can complete a work in 4 days, while 6 women and 3 men can complete the same work in 3 days. How many days will one woman and one man working together take to complete the same work?

Question 4:

In a library, the ratio of the number of mathematics books to that of physics books, is the same as the ratio of the number of physics books to that of chemistry books. If there are 144 mathematics books and 100 chemistry books, then the ratio of the total number of mathematics and physics books to the total number of chemistry and physics books is:

Question 5:

Karan and Arjun enter into a partnership with capital in the ratio $5: 7$.After 7 months Karan adds $60 \%$ of his capital, while After 7 months from starting Arjun withdraws $40 \%$ of his capital. What is the difference of the of the profit (in Rs. lakhs) of Karan and Arjun if the annual profit of Rs. $20.91$ lakhs?

Question 6:

Two cyclists start simultaneously from two points $A$ and $B$, their destinations being $B$ and $A$, respectively. After crossing each other, they precisely take 2 hours 33 minutes 36 seconds and 1 hour 26 minutes 24 seconds respectively to reach their destinations. What is the ratio of the speed of the first to that of the second cyclist?

Question 7:

A certain sum of money becomes $5$ times in a certain time period at $5%$ per annum interest, if the rate of interest becomes $20%$, then find how many times the amount will be in the same time period?

Question 8:

In a class of 92 students, the ratio of the number of boys to that of girls is $12: 11$. The average score of girls, in a test, is $33 \frac{1}{3} \%$ more than that of boys. If the average score of all students is 80 , then what is the average score of girls?

Question 9:

Anu fixes the selling price of an article at $25 \%$ above its cost of production. If the cost of production goes up by $20 \%$ and she raises the selling price by $10 \%$, then her percentage profit is (correct to one decimal place):

Question 10:

The average weight of 40 children of a class is $36.2 \mathrm{~kg}$. When three more children with weight $42.3 \mathrm{~kg}, 39.7 \mathrm{~kg}$ and $39.5 \mathrm{kg}$ join  the class, the average weight of the 43 children in the class is