$₹ 600$ is divided among A, B and C. $₹ 40$ more than $\frac{2}{5}$ th of A’ share, ₹ 20 more than $\frac{2}{7}$ th of B’s share and ₹ 10 more than $\frac{9}{17}$ th of C’s share are all equal. Then A’s share is

If $\tan \theta=\frac{2}{3}$, what is the value of $\frac{15 \sin ^{2} \theta-3 \cos ^{2} \theta}{5 \sin ^{2} \theta+3 \cos ^{2} \theta} ?$

From a window 15m high above the ground in a street, the angles of elevation and depression of the top and the foot of another house on the opposite side of the street are 30° and 45° respectively. The height of the opposite house is

What is the simplified value of $\frac{7}{\sec ^{2} \theta}+\frac{3}{1+\cot ^{2} \theta}+4 \sin ^{2} \theta ?$

The average of six numbers is x and the average of three of these is y. If the average of the remaining three is z, then

The value of $1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{2}}}}$ is

If $\cos \theta=-\frac{1}{2}$ and $\theta$ lies in third quadrant, then what will be the value of $\sin \theta+\tan \theta$

A bicycle rider covers his onward journey from A to B at 10 km/hr and during the return journey from B to A, he covers the same distance at 8 km/hr. If he finishes the onward and return journey in $4 \frac{1}{2}$ hours, then the total distance covered by him during the entire journey is

Two pipes A and B together can fill a cistern in 4 hours. If they had been opened separately, pipe B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?

A, B and C invested 13,000, 17,000 and 5,000 respectively in a business. At the end of the year, they earn a profit of 1,400. B’s share of profit is