In a certain class, (1/4)th of the total number of students who wear s

Let the number of boys = x

Then the number of girls = 2x

Total students = x + 2x = 3x

Number of boys who wears specs = \(\frac{1}{3}\)rd of the boys = \(\frac{x}{3}\) ... (1)


Let the total number of students who wears specs = y

Number of boys who wear specs = \(\frac{y}{4}\) ... (2)

Number of girls who wear specs = \(\frac{3y}{4}\) ... (3)


Number of boys who don't wear specs = \(1 - \frac{x}{3} = \frac{2x}{3}\)

From equations (1) and (2), \(\frac{x}{3} = \frac{y}{4}\). Therefore \(\frac{2x}{3} = 2 * \frac{x}{3} = 2 * \frac{y}{4} = \frac{2y}{4}\) ... (Equation 4)


Now, out of 2x girls, \(\frac{3y}{4}\) wear specs, and hence \(2x - \frac{3y}{4}\) don't wear specs

We know that from (1) and (2), \(\frac{x}{3} = \frac{y}{4}\) or \(x = \frac{3y}{4}\) and hence \(2x = \frac{6y}{4}\)


So the number of girls who don't wear specs = \(2x - \frac{3y}{4} = \frac{6y}{4} - \frac{3y}{4} = \frac{3y}{4}\) .... (Equation 5)



From 4 and 5, the ratio of Boys and girls who don't wear specs = \(\frac{2y}{4} : \frac{3y}{4}\) = 2 : 3



Option C

Arun Kumar

I think the question is not well written. "and (1/3)rd of the total number of boys in that class wears spectacles" does not mean that 1/3 of the boys wears spectacles but that the total number of Boys and Girls that wear spectacles equals (1/3) of the boys...

IMO it should have been "and (1/3)rd of the boys in that class wears spectacles"