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In a cricket tournament, 16 school teams participated. A sum of Rs 8000 is to be awarded among themselves as prize money. If the last placed team is awarded Rs 275 in prize money and the award increases by the same amount for successive finishing places, how much amount will the first place team receive?

0 2 Views | Posted 4 months ago
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    Answered by

    alok kumar singh | Contributor-Level 10

    4 months ago

    This is a Short Answer Type Questions as classified in NCERT Exemplar

    Sol:

    L e t     t h e     p r i z e     a m o u n t     g o t     b y     f i r s t     p l a c e     t e a m     b e           a Since,  the  prize  money  increases  by  the  same  amount  for  successive  finishing  places, T h e r e f o r e ,     t h e     s e r i e s     w i l l     b e     A . P . ∴                         a n = 2 7 5 ,     n = 1 6     a n d     S 1 6 = 8 0 0 0                             a n = a + ( n − 1 ) d                       2 7 5 = a + ( 1 6 − 1 ) ( − d )                             [ ?Common  difference  d  is(−)  as  the  series  is  decreasing ] ⇒             2 7 5 = a − 1 5 d                                                                                                                                               … ( i ) N o w       S n = n 2 [ 2 a + ( n − 1 ) d ] ⇒               S 1 6 = 1 6 2 [ 2 a + 1 5 ( − d ) ] ⇒       8 0 0 0 = 8 [ 2 a − 1 5 d ] = 2 a − 1 5 d = 1 0 0 0                                               … ( i i ) S o l v i n g     e q . ( i )     a n d     e q . ( i i )     w e     g e t                   a = 7 2 5     a n d     d = 3 0 H e n c e ,     t h e     r e q u i r e d     a w a r d     r e c e i v e d     b y     f i r s t     p l a c e     t e r m =       7 2 5 .

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