A boy takes a total of 11.5 hours in cycling to certain place and driving back. He would have gained 4 hours by driving both ways. What is the time he would take to cycle both ways?

11hr 30 min

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13hr 30 min

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15hr 30 min

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17hr 30 min

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None of these

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Solution

The correct option is C
15hr 30 min

$L e t x b e t h e s p e e d o f c y c l e . L e t y b e t h e s p e e d o f d r i v e . L e t D b e t h e t o t a l d i s t a n c e . T h e n \frac{D}{x} + \frac{D}{y} = \frac{23}{2} h r - - - - (1) \frac{D}{y} + \frac{D}{y} = \frac{23}{2} - 4 h r \frac{D}{y} = \frac{15}{4} - - - - (2) S u b s t i t u t e (2) i n (1) \frac{D}{x} + \frac{15}{4} = \frac{23}{2} \frac{D}{x} = \frac{23}{2} - \frac{15}{4} = \frac{46 - 15}{4} = \frac{31}{4} T i m e t a k e n f o r c y c l e o n e w a y i s \frac{31}{4} h r T i m e t a k e n t o c y c l e t o a n d f r o i s 2 \times \frac{31}{4} = \frac{31}{2} h r = 15 h r 30 m i n$

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