Question

The given figure represents the preferences of the students during breakfast in a hostel mess. If the total number of students in the mess is $540$, then with reference to the given figure, answer the following questions :
(i) What is the number of students who prefer coffee?
(ii) Whose number is greater, milk drinkers or orange juice drinkers and by what number?
(iii) What is the total number of students who drink mango shake or coffee? Is it equal to milk drinker?
(iv) Is the sum of all fractions in the given figure equal to 1?

Answer 1

(i) Total number of students $=540$
Ratio of students who prefer coffee $=\frac{1}{6}$
$\therefore$ Number of student prefer coffee
$=540\times \frac{1}{6}=90$students
(ii) Milk drinkers $=\frac{1}{3}$
Orange drinkers $=\frac{1}{4}$
LCM of $(3,4)=12$
$\frac{1}{3}=\frac{1\times 4}{3\times 4}=\frac{4}{12}$
$\frac{1}{4}=\frac{1\times 3}{4\times 3}=\frac{3}{12}$
$\Rightarrow \frac{4}{12}>\frac{3}{12}$
Number of milk drinkers $=540\times \frac{4}{12}=180$
Orange drinkers $=540\times \frac{3}{12}=135$
$=180-135=45$
$\therefore$ Milk drinkers are more than orange drinkers by number $=45$
(iii) Number of Mango shake drinkers $=540\times \frac{1}{6}=90$
Number of coffee drinkers
$=540\times \frac{1}{6}=90$
Total number of mango shake and coffee drinkers $=90+90=180$
Milk drinkers $=180$
Yes, it is equal to milk drinkers.
(iv) Sum of all fraction are :
$=\frac{1}{4}+\frac{1}{12}+\frac{1}{3}+\frac{1}{6}+\frac{1}{6}$

$(LCMof4,12,3,6,6=12)$

$=\frac{1\times 3}{4\times 3}+\frac{1\times 1}{12\times 1}+\frac{1\times 4}{3\times 4}+\frac{1\times 2}{6\times 2}+\frac{1\times 2}{6\times 2}$

$=\frac{3+1+4+2+2}{12}=\frac{12}{12}=1$
Yes, the sum of all the fractions are equal to $1.$