CBSE Class 10 Answered

A ball goes 64km upstream and 72km downstream in 14hrs. It goes 80km upstream and 96km downstream in 18hrs. Find the speed of ball in still water and speed of the stream.

Asked by Anjana S | 14 Jul, 2014, 05:12: PM

Expert Answer

$L e t space x space b e space t h e space s p e e d space o f space t h e space b a l l space a n d space y space b e space t h e space s p e e d space o f space t h e space s t r e a m. T h e n space x minus y space i s space t h e space s p e e d space o f space t h e space u p s t r e a m space a n d space x plus y space i s space t h e space s p e e d space o f space t h e space d o w n s t r e a m. T h e space b a l l space t r a v e l s space 64 space k m space u p s t r e a m space a n d space 72 space k m space d o w n s t r e a m space i n space 14 space h o u r s. T h u s comma space w e space h a v e comma fraction numerator 64 over denominator x minus y end fraction plus fraction numerator 72 over denominator x plus y end fraction equals 14... left parenthesis 1 right parenthesis T h e space b a l l space t r a v e l s space 64 space k m space u p s t r e a m space a n d space 72 space k m space d o w n s t r e a m space i n space 14 space h o u r s. T h u s comma space w e space h a v e comma fraction numerator 80 over denominator x minus y end fraction plus fraction numerator 96 over denominator x plus y end fraction equals 18.... left parenthesis 2 right parenthesis S u b s t i t u t i n g space fraction numerator 1 over denominator x minus y end fraction equals u space a n d space fraction numerator 1 over denominator x plus y end fraction equals v T h u s comma space e q u a t i o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis space c a n space b e space r e w r i t t e n space a s comma 64 u plus 72 v equals 14... left parenthesis 3 right parenthesis 80 u plus 96 v equals 18... left parenthesis 4 right parenthesis A g a i n space r e d u c i n g space t h e space a b o v e space s y s t e m comma space w e space h a v e comma 8 u plus 9 v equals 14 over 8... left parenthesis 5 right parenthesis 5 u plus 6 v equals 18 over 16... left parenthesis 6 right parenthesis M u l t i p l y i n g space e q u a t i o n left parenthesis 5 right parenthesis space b y space 5 space a n d space e q u a t i o n space left parenthesis 6 right parenthesis space b y space 8 space a n d space s u b t r a c t i n g space t h e space r e s u l t i n g space e q u a t i o n s o n e space f r o m space t h e space o t h e r space w e space h a v e comma 3 v equals 9 minus 70 over 8 rightwards double arrow 3 v equals fraction numerator 72 minus 70 over denominator 8 end fraction rightwards double arrow 3 v equals 2 over 8 rightwards double arrow 3 v equals 1 fourth rightwards double arrow v equals 1 over 12 S u b s t i t u t i n g space t h e space v a l u e space o f space v space i n space e q u a t i o n space left parenthesis 6 right parenthesis comma space w e space h a v e comma 5 u equals 18 over 16 minus 6 over 12 rightwards double arrow u equals 1 over 8 T h u s comma space w e space h a v e x minus y equals 8 x plus y equals 12 A d d i n g space t h e space a b o v e space t w o space e q u a t i o n s space w e space h a v e comma 2 x equals 20 rightwards double arrow x equals 10 rightwards double arrow y equals 2 T h u s space t h e space s p e e d space o f space t h e space b a l l space i s space 10 space k m divided by h r space a n d space t h e space s p e e d space o f space t h e space s t r e a m space i s space 2 space k m divided by h r.$