A circle is inscribed in an equilateral triangle of side 24 cm, touching its sides. What is the area of the remaining portion of the triangle?

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2 .

A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is

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3 .

In an examination, a student's average marks were 63. If he had obtained 20 more marks in Geography and 2 more marks in history, then his average would have been 65. How many subjects were there in the examination?

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4 .

A booster pump can be used for filling as well as emptying a tank. The capacity of the tank is 2400 $m^3 $. The emptying capacity of the tank is 10 $m^ 3$ /min higher than its filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump?

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5 .

A and B walking around a circular park at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, then how many times shall they meet each other before 9.30 a.m.?

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6 .

The profit is 320% of the cost price. The cost price increases by 25%, but the selling price remains constant. Find out approximately what percentage of the selling price is the profit?

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7 .

As per the observations of a person, standing exactly midway between two towers, the top of the two towers are at ang1le of elevation of 22.5° and 67.5°. What is the ratio of the height of the taller tower to the height of the shorter tower?

(Given that tan 22.5° = $\sqrt2$ - 1)

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8 .

Prasanth bought a car and paid 10 % less than the original price. He sold it with 30% profit on the price he had paid. What percentage of profit did he earn on the original price?

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9 .

If x = 8 + 3 $\sqrt 7$, then what is the value of $\sqrt x$ - $1 \over \sqrt x$ = ?

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10 .

Q as a percentage of P is equal to P as a percentage of (P + Q). Find Q as a percentage of P

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