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A carpenter was hired to build 192 window frames. The first day he made five frames and each day, thereafter he made two more frames than he made the day before. How many days did it take him to finish the job?

0 3 Views | Posted 4 months ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    4 months ago

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

    Sol:

    H e r e ,     f i r s t     t e r m     a = 5     a n d     t h e     c o m m o n     d i f f e r e n c e     d = 2     l e t     t h e     c a r p e n t e r     w i l l     t a k e     n     d a y s t o     f i n i s h     t h e     j o b .                                                   S n = 1 9 2                                                   S n = n 2 [ 2 a + ( n − 1 ) d ]                                               1 9 2 = n 2 [ 2 × 5 + ( n − 1 ) 2 ] ⇒                       1 9 2 × 2 = n [ 1 0 + 2 n − 2 ]             ⇒ 3 8 4 = n ( 2 n + 8 ) ⇒                                   3 8 4 = 2 n 2 + 8 n             ⇒ 2 n 2 + 8 n − 3 8 4 = 0 ⇒ n 2 + 4 n − 1 9 2 = 0         ⇒ n 2 + 1 6 n − 1 2 n − 1 9 2 = 0 ⇒ n ( n + 1 6 ) − 1 2 ( n + 1 6 ) = 0         ⇒ ( n − 1 2 ) ( n + 1 6 ) = 0 ⇒                             n = 1 2                             [ ? n ≠ − 1 6 ] H e n c e ,     t h e     r e q u i r e d     n u m b e r     o f     d a y s = 1 2 .

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