Question

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?

Answer 1

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

Let the carpenter will take n days to finish the job

S_n = 192

S_n = `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.