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ICSE Class 8 Answered

A , B and C working together take 30 mins to address a pile of envelopes .A and B working together would take 40 mins ; A and C together would take 45 mins .how long would each take working alone?
Asked by bhavyaaj | 28 Dec, 2014, 01:55: PM
answered-by-expert Expert Answer
G i v e n space t h a t space A comma space B space a n d space C space t o g e t h e r space f i n s h space t h e space w o r k space i n space 30 space m i n u t e s. T h e r e f o r e comma A plus B plus C space apostrophe s space 1 space m i n u t e apostrophe s space w o r k equals 1 over 30... left parenthesis 1 right parenthesis A space a n d space B space t o g e t h e r space f i n i s h space t h e space w o r k space i n space 40 space m i n u t e s. T h e r f o r e comma space A plus B apostrophe s space 1 space m i n u t e space w o r k equals 1 over 40... left parenthesis 2 right parenthesis A space a n d space C space t o g e t h e r space f i n i s h space t h e space w o r k space i n space 45 space m i n u t e s. T h e r f o r e comma space A plus C apostrophe s space 1 space m i n u t e space w o r k equals 1 over 45... left parenthesis 3 right parenthesis A d d i n g space e q u a t i o n s space left parenthesis 2 right parenthesis space a n d space left parenthesis 3 right parenthesis comma space w e space h a v e comma 2 A plus B plus C space apostrophe s space 1 space m i n u t e space w o r k equals 1 over 40 plus 1 over 45 equals 17 over 360... left parenthesis 4 right parenthesis S u b t r a c t i n g space e q u a t i o n left parenthesis 1 right parenthesis space f r o m space e q u a t i o n space left parenthesis 4 right parenthesis comma space w e space h a v e comma open parentheses 2 A plus B plus C minus A minus B minus C close parentheses apostrophe s space 1 space m i n u t e space w o r k equals 17 over 360 minus 1 over 30 equals 1 over 72 rightwards double arrow A apostrophe s space 1 space m i n u t e space w o r k equals 1 over 72... left parenthesis 5 right parenthesis S u b t r a c t i n g space e q u a t i o n left parenthesis 5 right parenthesis space f r o m space e q u a t i o n space left parenthesis 2 right parenthesis comma space w e space h a v e comma left parenthesis A plus B minus A right parenthesis apostrophe s space 1 space m i n u t e space w o r k equals 1 over 40 minus 1 over 72 equals 1 over 90 rightwards double arrow B apostrophe s space 1 space m i n u t e space w o r k equals 1 over 90... left parenthesis 6 right parenthesis S u b t r a c t i n g space e q u a t i o n left parenthesis 5 right parenthesis space f r o m space e q u a t i o n space left parenthesis 3 right parenthesis comma space w e space h a v e comma left parenthesis A plus C minus A right parenthesis apostrophe s space 1 space m i n u t e space w o r k equals 1 over 45 minus 1 over 72 equals 1 over 120 rightwards double arrow C apostrophe s space 1 space m i n u t e space w o r k equals 1 over 120 T h u s space A space c a n space f i n i s h space t h e space w o r k space i n space 72 space m i n u t e s comma space B space a n c space f i n i s h space t h e space w o r k space i n space 90 space m i n u t e s space a n d space C space c a n space f i n i s h space t h e space w o r k space i n space 120 space m i n u t e s.
Answered by Vimala Ramamurthy | 28 Dec, 2014, 06:17: PM
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