In a class there are 60 students. The following pie diagram shows the number of students according to blood-group. There are 8 students having blood-group A, 18 students having blood-group O. Students having B group are represented by $120^{o}$ , find the number of students having AB blood-group :

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Solution

The correct option is A 14
Let the number of students with blood group $B$ be $x$ and $A B$ be $y$
The angle subtended by blood group $B$ is $120^{0}$ , so the angle subtended by remaining three blood groups will be $360^{0} - 120^{0} = 240^{0}$
$\Rightarrow \frac{18 + 8 + y}{x} = \frac{240}{120} = 2$
$\Rightarrow 26 + y = 2 x$
We have $x + y + 18 + 8 = 60$
$\Rightarrow x + y = 34$
Substitute $y = 2 x - 26$ in above equation , we get $x + 2 x - 26 = 34$
$\Rightarrow x = 20, y = 14$
Therefore number of students having $A B$ blood group is $14$
So the correct option is $A$

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Similar questions

In a medical examination of students of a class, the following blood groups are recorded:

Blood group A AB B O

No. of students 10 13 12 5

A student is selected at random from the class. Find the probability that he/she has blood group B.

A group of students from a school decided to donate blood. The blood groups of 16 students of class X are recorded as follows:

A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, AB. Find the probability of blood group

a) O

b) A

Blood group	A	B	O	AB
Number of students	11	9	14	6

Blood group	A	B	AB	O
Number of students	11	15	8	6

\frac{13}{20}

\frac{3}{8}

\frac{1}{5}

\frac{11}{40}

\begin{matrix} Blood group & A + & A B - & B - & O + Number of & 10 & 13 & 12 & 5 students \end{matrix}

B -

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