Multi-concept problems combining algebra, geometry and reasoning.
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Q1 · Higher Order Thinking · MEDIUM
A rectangle has length L cm and breadth B cm. If the length is increased by 20% and the breadth is decreased by 10%, the area increases by 8 sq cm. If the length is decreased by 10% and the breadth is increased by 20%, the area increases by 8 sq cm. Find the original area of the rectangle in sq cm.
Q2 · Higher Order Thinking · EASY
In triangle ABC, angle B = 90°. A circle with center O passes through points A, B and C. If AB = 6 cm and BC = 8 cm, find the radius of the circle in cm.
Q3 · Higher Order Thinking · MEDIUM
A two-digit number is such that the product of its digits is 24. When 18 is subtracted from the number, the digits interchange their places. Find the sum of the digits of the number.
Q4 · Higher Order Thinking · HARD
A circle is inscribed in a trapezium ABCD where AB is parallel to CD. The sides AB = 14 cm, CD = 6 cm, and the non-parallel sides BC = AD. A circle touches all four sides. If the area of the trapezium is 60 sq cm, find the radius of the inscribed circle in cm.
Q5 · Higher Order Thinking · HARD
A clock shows 3:00. What is the angle between the hour hand and the minute hand?