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Monday, June 29, 2015

UPSC Maths Problems Challenge : A Problem A Day! (Day 17)

For the last 16 days,we have either been solving mostly aptitude-based Maths problems (from interviews or UPSC Mains) and I was giving it a thought that we are completely skipping Prelims,which require basic,strategic and carefully planned preparation.Finally,I have started solving problems from the Preliminary Examinations conducted by UPSC.Here is the first problem.Read on to find out the solution.

Today's Problem(29/06/2015)

Question Credit :

(Prelim 1998) LMNOP is a semicircle with centre at R and diameter LP. LSR and RQP are also semi-circles with centres at T and U respectively and diameters LR=RP=1/2 LP. What is the ratio of perimeter of LMNOP and LSRQP?

Perimieter of LMNOP = (2πr/2) sq.units = πr sq.units. =  (π * PR) sq.units = (π * 2TR) sq.units = 2πTR sq.units......Eqn 1.

Perimeter of LSRQP = Perimeter of semi-circle LSR (not inclusive of diameter) + Perimeter of semi-circle PQR (not inclusive of diameter) = {(π * TR) + (π * UR)} sq.units
 = {(π * TR) + (π * TR)} sq.units = 2πTR sq.units......Eqn 2.
From equations 1 and 2,we have Perimeter of LMNOP : Perimeter of LSRQP = 1 : 1

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