Suman is given an aptitude test containing 80 problems, each carrying I mark to be tackled in 60 minutes. The problems are of 2 types; the easy ones and the difficult ones. Suman can solve the easy problems in half a minute each and the difficult ones in 2 minutes each. (The two type of problems alternate in the test). Before solving a problem, Suman must spend one-fourth of a minute for reading it. What is the maximum score that Suman can get if he solves all the problems that he attempts?

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Solution

The correct option is C 53
$A s s u m i n g t h a t a l l t h e p r o b l e m s s u m a n s o l v e s a r e r i g h t, m a r k s e a r n e d p e r m i n u t e s o l v i n g e a s y p r o b l e m = \frac{1}{3 / 4} = \frac{4}{3} m a r k s e a r n e d p e r m i n u t e s o l v i n g d i f f i c u l t p r o b l e m = \frac{1}{9 / 4} = \frac{4}{9} s i n c e w e h a v e t o m a x i m i z e t h e m a r k s, w e w i l l s o l v e a l l t h e e a s y p r o b l e m s f i r s t . m a r k s e a r n e d b y s o l v i n g e a s y p r o b l e m s = 40, t i m e s p e n t = \frac{3}{4} * 40 = 30 m i n u t e s t i m e l e f t f o r d i f f i c u l t p r o b l e m s = 30 m i n u t e s, p r o b l e m s s o l v e d = \frac{30}{9 / 4} = 13, m a r k s e a r n e d = 13, t o t a l m a r k s = 40 + 13 = 53$

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