If \( p \) varies directly as \( q \) and inversely as square of \( r \), what is the percentage increase in \( p \) due to an increase in \( q \) by 20% and a decrease in \( r \) by 20%?
A person agrees to work for 30 days, on a condition that for every day's work he should receive ₹500, and that for every day's absence from work he should forfeit ₹100. At the end of the time he received ₹11,400. How many days did he work?
A person bought a chair and a table for ₹750. He sold the chair at a gain of 5% and the table at a gain of 20%. He gained 16% on the whole. What is original cost of table?
A person rode one-third of a journey at 60 km/hr, one-third at 50 km/hr and the rest at 40 km/hr. Had the person ridden half of the journey at 60 km/hr and the rest at 40 km/hr, he would have taken 4 minutes longer to complete the journey. What distance did the person ride?
If \( 14\sin^{2}\theta + 10\cos^{2}\theta = 11 \) where \( 0^{\circ} < \theta < 90^{\circ} \), then what is the value of \( \tan\theta + \cot\theta \)?
A ladder 10 m long reaches a point 10 m below the top of a vertical flagstaff. From foot of the ladder, the elevation of top of the flagstaff is \( 60^{\circ} \). What is the height of flagstaff?
