A carpenter was hired to build 192 window frames. The first day he made five frames and each day there after he made two more frames than he made the day before. How many days did it take him to finish the job? [NCERT EXEMPLAR]
Given: Carpenter was hired to build 192 frames. He made 5 frames on first day and two more frames for every next day
To find: Number of days taken by him to build 192 frames
According to question:
A.P. will be 5, 7, 9,………………………………
⇒ Sn = 192, a = 5 and d = 7 – 5 = 2
Formula used:
where a is first term, d is common difference and n is number of terms in an A.P.
Therefore,
⇒ n2 + 16n – 12n + 192 = 0
⇒ n(n + 16) – 12(n + 16) = 0
⇒ (n + 16)(n – 12) = 0
⇒ n = –16 or 12
n is number of days and it cannot be negative
Therefore, we will take value of n = 12
Hence, he will take 12 days to build 192 frames