Question

In a garden there are two plants. One plant is \( 44 \mathrm{~cm} \) tall and the other is \( 80 \mathrm{~cm} \) tall. The first. plant grows \( 3 \mathrm{~cm} \) in every 2 months and the second \( 5 \mathrm{~cm} \) in every 6 months. The number of months after which the two plants will have equal height is .

Answer 1

First plant height = 44 cm and it grows 3 cm in every 2 months. 

\(\therefore\) Common difference = 3/2

After 1^st month plant height = 44 + 3/2 = (88 + 3)/2 = 91/2

After n^th month first plant height

 = 91/2 + (n - 1)3/2.

Second plant height  = 80 cm and it grows 5cm in every 6 months.

 \(\therefore\) Common difference = 5/6

After 1^st month plant height = 80 + 5/6 = 485/6

After n^th month second plant height

= 485/6 + (n - 1)5/6

Let both plants have equal height after n month.

Therefore, 91/2 + (n -1) 3/2 = 485/6 + (n - 1) 5/6

⇒ (n -1) (3/2 - 5/6) = 485/6 - 91/2 = (485-273)/6 = 212/6

⇒ (n –1)=212/6 x 6/(9 - 5) = 212/4 = 53

⇒ n = 53 + 1 = 54

\(\therefore\)  After 54^th month both plants will have equal height.