In a forest, a certain number of apes equal to the square of one-eight of the total
number of their groups are playing and having great fun. The rest of them are twelve
in number and are on an adjoining hill. The echo of their shrieks from the hills frightens
them. They come and join the apes in the forest and play with enthusiasm. What is the
total number of apes in the forest?
Answers
Given : a certain number of apes equal to the square of one-eight of the total number of their groups are playing and having great fun.
The rest of them are twelve in number and are on an adjoining hill
The echo of their shrieks from the hills frightens them.
To Find : total number of apes in the forest
Solution:
Total Number = T
square of one-eight of the total number = (T/8)²
The rest of them are twelve n number = 12
(T/8)² + 12 = T
=> T² + 12 * 64 = 64T
=> T² - 64T + 12 * 64 = 0
=> T² - 16T - 48T + 12 * 64 = 0
=> T ( T - 16) - 48 ( T - 16) = 0
=> ( T - 48) ( T - 16) = 0
=> T = 48 , T = 16
48 or 16
(T/8)² = (48/8)² = 36 + 12 = 48
(T/8)² = (16/8)² = 4 + 12 = 16
The echo of their shrieks from the hills frightens them.
Hence we take higher value
Hence total number of apes in the forest = 48
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Answer:
Given : a certain number of apes equal to the square of one-eight of the total number of their groups are playing and having great fun.
The rest of them are twelve in number and are on an adjoining hill
The echo of their shrieks from the hills frightens them.
To Find : total number of apes in the forest
Solution:
Total Number = T
square of one-eight of the total number = (T/8)²
The rest of them are twelve n number = 12
(T/8)² + 12 = T
=> T² + 12 * 64 = 64T
=> T² - 64T + 12 * 64 = 0
=> T² - 16T - 48T + 12 * 64 = 0
=> T ( T - 16) - 48 ( T - 16) = 0
=> ( T - 48) ( T - 16) = 0
=> T = 48 , T = 16
48 or 16
(T/8)² = (48/8)² = 36 + 12 = 48
(T/8)² = (16/8)² = 4 + 12 = 16
The echo of their shrieks from the hills frightens them.
Hence we take higher value
Hence total number of apes in the forest = 48