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Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed

(a) In English and Mathematics but not in Science

(b) In Mathematics and Science but not in English

(c) In Mathematics only

(d) In more than one subject only

0 6 Views | Posted 4 months ago
Asked by Shiksha User

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    Answered by

    Vishal Baghel | Contributor-Level 10

    4 months ago

    L e t     t h e     n u m b e r     o f     s t u d e n t s     p a s s e d     i n     M a t h e m a t i c s     M , E     b e     i n     E n g l i s h     a n d     S     b e     i n     S c i e n c e . T h e n     n ( U ) = 1 0 0 ,     n ( M ) = 1 2 ,     n ( E ) = 1 5 ,     n ( S ) = 8 n ( E ∩ M ) = 6 ,     n ( M ∩ S ) = 7 ,     n ( E ∩ S ) = 4     a n d     n ( E ∩ M ∩ S ) = 4 L e t     u s     d r a w     a     v e n n     d i a g r a m .     A c c o r d i n g     t o     t h e     v e n n     d i a g r a m ,     w e     g e t                       a + b + d + e = 1 5                                                                                 … ( i )                       b + c + e + f = 1 2                                                                                 … ( i i )                       d + e + f + g = 8                                                                                 … ( i i i )                               n ( E ∩ M ) = 6           ∴     b + e = 6                               … ( i v )                                 n ( M ∩ S ) = 7           ∴     e + f = 7                               … ( v )                                     n ( E ∩ S ) = 4           ∴     d + e = 4                               … ( v i )               n ( E ∩ M ∩ S ) = 4           ∴     e = 4                                             … ( v i i ) F r o m     e q n . ( i v )     a n d     ( v i i )     w e     g e t     b + 4 = 6         ∴ b = 2 F r o m     e q n . ( v )     a n d     ( v i i )     w e     g e t     4 + f = 7         ∴ f = 3 F r o m     e q n . ( v i )     a n d     ( v i i )     w e     g e t     d + 4 = 4         ∴ d = 0 F r o m     e q n . ( i )     w e     g e t     a + b + d + e = 1 5 ⇒                                 a + 2 + 0 + 4 = 1 5         ⇒ a = 9 F r o m     e q n . ( i i )     w e     g e t     b + c + e + f = 1 2 ⇒                                 2 + c + 4 + 3 = 1 2         ⇒ c = 3 F r o m     e q n . ( i i i )     w e     g e t     d + e + f + g = 8 ⇒                                 0 + 4 + 3 + g = 8         ⇒ g = 1 ∴ ( i ) N u m b e r     o f     s t u d e n t s     w h o     p a s s e d     i n     E n g l i s h     a n d     M a t h e m a t i c s     b u t     n o t     i n     S c i e n c e ,     b = 2       ( i i ) N u m b e r     o f     s t u d e n t s     w h o     p a s s e d     i n     M a t h e m a t i c s     a n d     S c i e n c e     b u t     n o t     i n     E n g l i s h ,     f = 3     ( i i i ) N u m b e r     o f     s t u d e n t s     w h o     p a s s e d     i n     M a t h e m a t i c s     o n l y ,     c = 3 .

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