20 boys and 32 girls from a group for social work. During their membership same number of boys and girls joined the group. How many members does the group have now if the ratio of boys to girls is respectively? Select one: a. 68 b. 84 c. 86 d. 75
Answers
Question:
20 boys and 32 girls form a group for social work. During their membership drive same no. of boys and girls joined the group. How many members does the group have now, if the ratio of boys to girls is 3:4 respectively?
75
86
68
82
None of these
Answer:
(b) 84
Step-by-step explanation:
Define x:
Let the number of boys that joined be x
The number of girls that joined = number of boys that joined = x
Solve x:
The ratio became 3 : 4
(20 + x) / (32 + x ) = 3/4
4(20 + x) = 3(32 + x)
80 + 4x = 96 + 3x
x = 96 - 80
x = 16
16 boys and 16 girls joined the group
Find the number of people in the group now:
boys = 20 + 16 = 36
girls = 32 + 16 = 48
Total = 36 + 48 = 84
Answer: There are 84 people in the group now.
The question is incomplete.
However,
Given:
Boys = 20
Girls = 32
Same number of boys and girls joined the group
Boy : Girl = 3 : 4
To find:
The number of members in the group.
Solution:
The number of boys joined the group = The number of girls joined the group
Hence,
( 20 + The number of boys/girls joined the group ) / ( 32 + The number of boys/girls joined the group ) = 3/4
4 ( 20 + The number of boys/girls joined the group ) = 3 ( 32 + The number of boys/girls joined the group )
The number of boys/girls joined the group = 96 - 80
Therefore,
The number of boys/girls joined the group = 16
16 boys joined the group
16 girls joined the group
The total number of people in the group,
20 + 16 + 32 + 16
The total number of people in the group = 84