OE


We are given that the girls are more than boys in a class. Each boy collected 5 and
each girl collected 3 flowers. A total of 46 flowers were collected.
We have to find the number of girls in the class.
Let’s assume there are x girls and y boys in the class such that x > y.
According to the question,
3𝑥 + 5𝑦 = 46 (eqn.1)
Since, the number of boys and girls has to be a positive integer value and options are
given for the number of girls so we can check which answer choice gives me a
positive integer value for the number of boys in the class.


A. 6
If 𝑥 = 6 then from equation 1 we get,
3 × 6 + 5𝑦 = 46
i.e. 18 + 5𝑦 = 46
i.e. 5𝑦 = 28
i.e. 𝑦 =28/5
which is not an integer.
Hence, A is not the answer.

B. 10
If 𝑥 = 10 then from equation 1 we get,
30 + 5𝑦 = 46
i.e. 5𝑦 = 16
i.e. 𝑦 =16/5
which is not an integer.
Hence, B is not the answer.

C. 12
If 𝑥 = 12 then from equation 1 we get,
36 + 5𝑦 = 46
i.e. 5𝑦 = 10
i.e. 𝑦 = 2 which is a positive integer.
Hence, C is the answer.

D. 14
If 𝑥 = 14 then from equation 1 we get,
42 + 5𝑦 = 46
i.e. 5𝑦 = 4
i.e. 𝑦 =4/5
which is not an integer.
Hence, D is not the answer.
Ans. (C)
_________________

12 x 3 = 36
46-36 = 10
so according to the conditions 12 girls and 2 boys . dont need so much of calculation..pick from the options and test the logic. thanks

Solving for the equation 5B + 3G = 46
We have only 2 possibilities where G>B
B G
2 12
5 7

We can solve it directly using the options
if number of girls is 6 , flowers collected by them will be 3 x 6 = 18 but 28 flowers cannot be collected by boys since it should be multiple of 5
if number of girls is 10 , flowers collected by them will be 3 x 10 = 30 but 16 flowers cannot be collected by boys since it should be multiple of 5
if number of girls is 12 , flowers collected by them will be 3 x 12 = 36 => possible
hence c is the answer