# 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 - Mathematics

Sum

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?

#### Solution

Here, first term a = 5 and the common difference d = 2

Let the carpenter will take n days to finish the job

Sn = 192

Sn = n/2[2a + (n - 1)d]

192 = n/2[2 xx 5 + (n - 1)2]

⇒ 192 × 2 = n[10 + 2n – 2]

⇒ 384 = n(2n + 8)

⇒ 384 = 2n2 + 8n

⇒ 2n2 + 8n – 384 = 0

⇒ n2 + 4n – 192 = 0

⇒ n2 + 16n – 12n – 192 = 0

⇒ n(n + 16) – 12(n + 16) = 0

⇒ (n – 12)(n + 16) = 0

⇒ n = 12   ....[∵ n ≠ –16]

Hence, the required number of days = 12.

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Chapter 9: Sequences and Series - Exercise [Page 161]

#### APPEARS IN

NCERT Exemplar Class 11 Mathematics
Chapter 9 Sequences and Series
Exercise | Q 5 | Page 161
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