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?

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Alok Kumar Singh | Contributor-Level 10

8 months ago

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

Sol:

$\begin{array}{l} H e r e, f i r s t t e r m a = 5 a n d t h e c o m m o n d i f f e r e n c e d = 2 l e t t h e c a r p e n t e r w i l l t a k e n d a y s \\ t o f i n i s h t h e j o b . \\ S_{n} = 192 \\ S_{n} = \frac{n}{2} [2 a + (n - 1) d] \\ 192 = \frac{n}{2} [2 * 5 + (n - 1) 2] \\ \Rightarrow 192 * 2 = n [10 + 2 n - 2] \Rightarrow 384 = n (2 n + 8) \\ \Rightarrow 384 = 2 n^{2} + 8 n \Rightarrow 2 n^{2} + 8 n - 384 = 0 \\ \Rightarrow n^{2} + 4 n - 192 = 0 \Rightarrow n^{2} + 16 n - 12 n - 192 = 0 \\ \Rightarrow n (n + 16) - 12 (n + 16) = 0 \Rightarrow (n - 12) (n + 16) = 0 \\ \Rightarrow n = 12 [? n \neq - 16] \\ H e n c e, t h e r e q u i r e d n u m b e r o f d a y s = 12 . \end{array}$

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Start with

(1) $\bar{E} : \frac{6!}{2!} = 360$

(2) $\bar{G E} : \frac{5!}{2!},$ $\bar{G N} : \frac{5!}{2!}$

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