Question Detail

In a hotel, 60% had vegetarian lunch while 30% had non-vegetarian lunch and 15% had both type of lunch. If 96 people were present, how many did not eat either type of lunch ?

Answer: Option D

Explanation:

\begin{aligned}
n(A) = \left(\frac{60}{100}*96\right) = \frac{288}{5} \\
n(B) = \left(\frac{30}{100}*96\right) = \frac{144}{5} \\
n(A\cap B) = \left(\frac{15}{100}*96\right) = \frac{72}{5} \\
\text{People who have either or both lunch} \\
n(A\cup B) = \frac{288}{5}+\frac{144}{5}-\frac{72}{5} \\
= \frac{360}{5} = 72
\end{aligned}

So People who do no have either lunch were = 96 -72
= 24

1. In an examination, 34% of the students failed in mathematics and 42% failed in English. If 20% of the students failed in both the subjects, then find the percentage of students who passed in both the subjects.

Answer: Option C

Explanation:

Failed in mathematics, n(A) = 34
Failed in English, n(B) = 42
\begin{aligned}
n(A\cup B) = n(A)+n(B)-n(A\cap B) \\
= 34+42-20 = 56 \\
\text{Failed in either or both subjects are 56} \\
\text{Percentage passed = }(100-56)\% \\
= 44\%
\end{aligned}

2. How many litres of pure acid are there in 8 litres of a 20% solution

Answer: Option B

Explanation:

Question of this type looks a bit typical, but it is too simple, as below...

It will be 8 * 20/100 = 1.6

3. Raman's salary was decreased by 50% and subsequently increased by 50%. How much percent does he loss.

Answer: Option D

Explanation:

Let the origianl salary = Rs. 100

It will be 150% of (50% of 100)
= (150/100) * (50/100) * 100 = 75

So New salary is 75, It means his loss is 25%

4. A batsman scored 120 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets.

Answer: Option B

Explanation:

Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 120 - (60)
= 60

Now, we need to calculate 60 is what percent of 120.

=> 60/120 * 100 = 50 %

5. A housewife saved Rs. 2.50 in buying an item on sale. If she spent Rs. 25 for the item, approximately how much percent she saved in the transaction

Answer: Option A

Explanation:

Actual Price = Rs.25 + Rs.2.50 = Rs.27.5

Saving = Rs.2.5

\begin{aligned}\text{Percentage Saving = }\dfrac{2.5}{27.5}\times 100 \\
= \dfrac{250}{27.5} = \dfrac{2500}{275}\\
= \dfrac{100}{11} = 9\dfrac{1}{11}\% \approx 9\%\end{aligned}