UPSC Prelims 1998 · General Studies
Question 133: Basic Numeracy
LMNOP is a semi-circle with centre at R and diameter LP; LSR and RQP are also semi-circles with centres at T and U and diameters LR = RP = 1⁄2 LP. The ratio of perimeters of LMNOP and LSRQP is
AnswerThe answer is (b).
Let LP = d. The semicircle LMNOP has a curved length of pi d/2. LSRQP is made of two semicircles of diameter d/2, each of length pi (d/2)/2 = pi d/4, together pi d/2. The curved lengths are equal, and if the straight line LP is added to each outline the perimeters are still equal, so the ratio is 1 : 1.
Why each option is right or wrong
- (a) The perimeters are equal, not in the ratio 3 : 4.
- (b) Right: both equal pi d/2 (and the same plus d if closed).
- (c) The perimeters are equal, not in the ratio 4 : 3.
- (d) The perimeters are equal, not in the ratio 5 : 4.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 1998, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.