Question

Direction: In a birthday party, some children are invited who like at least one of the three dishes, noodles, fried rice, and dosa. The number of children who like noodles is $150$, and all three dishes are liked by $12\%$ of the children who like noodles. The ratio of the number of children who like fried rice and dosa is $2:3$, and the sum of those children who like fried rice and those who like dosa is $150\%$ more than the number of students who like noodles. The number of children who like both noodles and dosa is $18\%$ of the number of children who like noodles. The ratio of the players who like both noodles and dosa to the number of children who like both fried rice and dosa is $3:4$. The total number of children who like both noodles and fried rice and those who like both fried rice and dosa is equal to one-third of those who like dosa.

Find the average number of children who like only one dish.

• A. $105$
• B. $113$
• C. $110$
• D. $120$

Answer 1

The correct option is B $113$

Number of children who like noodles $=150$

Number of children who like all three dishes $=12\%$ of $150=18$

Let the number of children who like fried rice be $2x$.

So, the number of children who like dosa $=3x$

So, the Venn diagram of the given data will be as shown below.



So,

$2x+3x=\frac{250}{100}\times 150=375\Rightarrow x=75$

So, the number of children who like fried rice $=150$

Number of children who like dosa $=3\left(75\right)=225$

Number of children who like both noodles and dosa $=18\%$ of $150=27$

So, the number of children who like only noodles and dosa $=27–18=9$

Let the number of children who like only fried rice and dosa be ‘$z$’.

So,

$\frac{27}{18+z}=\frac{3}{4}\Rightarrow 18+z=36\Rightarrow z=18$

Let the number of children who like only fried rice and noodles be ‘$y$’.

So,

$18+y+18=\frac{1}{3}\times 225=75$ $\Rightarrow 36+y=75\Rightarrow y=39$

Hence, the number of children who only like noodles only $=150–(9+18+39)=84$

Number of children who only like fried rice $=150–(39+18+18)=75$

Number of children who only like dosa $=225–(9+18+18)=225–45=180$

IMAGE

Hence, the required average $=\frac{84+75+180}{3}=\frac{339}{3}=113$

Hence, option (C) is the correct answer.