The sum of the radii of two circles is 75 cm and difference in their…
2025
The sum of the radii of two circles is 75 cm and difference in their circumferences is 44 cm. The radii of the circles are : (use π = 22/7)
- A.
40 cm, 35 cm
- B.
41 cm, 34 cm
- C.
39 cm, 36 cm
- D.
44 cm, 31 cm
Attempted by 3 students.
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Correct answer: B
Concept: The circumference of a circle is C = 2πr. For two circles, the DIFFERENCE of their circumferences is directly proportional to the difference of their radii: C1 − C2 = 2π(r1 − r2). A "sum of radii" condition together with a "difference of circumferences" condition converts into a standard pair of linear equations in r1 and r2.
Let the two radii be r1 and r2. The given sum condition is r1 + r2 = 75 cm.
The given difference-of-circumferences condition is 2π(r1 − r2) = 44 cm. Substituting π = 22/7: 2 × (22/7) × (r1 − r2) = 44.
Simplify the left side: (44/7)(r1 − r2) = 44, so r1 − r2 = 44 × (7/44) = 7 cm.
Solve the two linear equations together — r1 + r2 = 75 and r1 − r2 = 7. Adding them: 2r1 = 82, so r1 = 41 cm. Subtracting them: 2r2 = 68, so r2 = 34 cm.
Cross-check: 41 + 34 = 75 cm, matching the given sum. Also 2 × (22/7) × (41 − 34) = 2 × (22/7) × 7 = 44 cm, matching the given circumference difference. Both conditions hold together only for this pair of radii.
Hence the radii of the two circles are 41 cm and 34 cm.