Percentage Questions and Answers

Q: 44% of the students in the class are females and the number of male students is 42. Find the total number of students in the class.

The class has 75 students.If 44% are females, the males are \(100 - 44 = 56\%\) of the class, and they number 42.\[ \begin{aligned} 0.56 \times N &= 42 \\ N &= \frac{42}{0.56} = 75 \end{aligned} \]Check: 44% of 75 is 33 females, and \(33 + 42 = 75\).Taking 42 as 44% of the class (the female share) gives about 95, which is not offered. 70 would leave 28 females, 40% of the class, and 65 would make the males alone almost 65% of it. 45 would leave only 3 females, under 7% of the class.

Q: Neha bought a cooler for ₹ 3,300 including a tax of 10%. Then the price of the cooler before tax is :

The price before tax is ₹ 3,000.The price including tax is 110% of the price before tax. Let the price before tax be \(P\):\[ \begin{aligned} 1.10P &= 3300 \\ P &= \frac{3300}{1.10} = 3000 \end{aligned} \]Check: 10% of 3,000 is 300, and 3,000 + 300 = 3,300. The trap is ₹ 2,970, which is 3,300 minus 10% of 3,300: the tax is 10% of the pre-tax price, not of the total. ₹ 3,030 and ₹ 2,700 come from adding or subtracting the tax amount the wrong way.

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41.

44% of the students in the class are females and the number of male students is 42. Find the total number of students in the class.

A.70
B.65
C.75
D.45

Exam Year(s)

MP Lab Technician - 2015,

Answer: C

The class has 75 students.

If 44% are females, the males are \(100 - 44 = 56\%\) of the class, and they number 42.

\[ \begin{aligned} 0.56 \times N &= 42 \\ N &= \frac{42}{0.56} = 75 \end{aligned} \]

Check: 44% of 75 is 33 females, and \(33 + 42 = 75\).

Taking 42 as 44% of the class (the female share) gives about 95, which is not offered. 70 would leave 28 females, 40% of the class, and 65 would make the males alone almost 65% of it. 45 would leave only 3 females, under 7% of the class.

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42.

Neha bought a cooler for ₹ 3,300 including a tax of 10%. Then the price of the cooler before tax is :

A.₹ 2,700
B.₹ 2,970
C.₹ 3,000
D.₹ 3,030

Exam Year(s)

MPPSC Forest Service - 2023,

Answer: C

The price before tax is ₹ 3,000.

The price including tax is 110% of the price before tax. Let the price before tax be \(P\):

\[ \begin{aligned} 1.10P &= 3300 \\ P &= \frac{3300}{1.10} = 3000 \end{aligned} \]

Check: 10% of 3,000 is 300, and 3,000 + 300 = 3,300. The trap is ₹ 2,970, which is 3,300 minus 10% of 3,300: the tax is 10% of the pre-tax price, not of the total. ₹ 3,030 and ₹ 2,700 come from adding or subtracting the tax amount the wrong way.

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43.

Three candidates contested an election and received \(1136, 7636\) and \(11628\) votes respectively. What percentage of the total votes did the winning candidate get?

A.57 %
B.60 %
C.65 %
D.90 %

Answer: A

Total number of votes polled \(= (1136 + 7636 + 11628) = 20400.\)

\(\therefore\) Requried percentage \(= (\frac{11628}{20400} \times 100)\)% \(= 57\)%

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44.

A student multiplied a number by \(\frac{5}{6}\) instead of \(\frac{6}{5}\). What is the percentage
error in the calculation?

A.44 %
B.30.56 %
C.15.28 %
D.22 %

Answer: B

The number be 30

When the student multiplied it by \(\frac{5}{6}\), ⇒ original result \(= \frac{5}{6} \times 30 = 25\)

When the student multiply it by \(\frac{6}{5}\), ⇒ New result \(= \frac{6}{5} \times 30 = 36\)

⇒ Percentage error in calculation \(= \frac{(36-25)}{36} \times 100 \)

\(\Rightarrow \frac{1100}{36} = 30.56\)

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45.

In an election between two candidates, one got \(55\) % of the total valid votes, \(55\)% of the votes were invalid. If the total number of votes was \(7500\), the number of valid votes that the other candidate got, was:

A.2700
B.2900
C.3000
D.3100

Answer: A

Number of valid votes \(= 80\) % of \(7500 = 6000.\)

\(\therefore \) Valid votes polled by other candidate \(= 45\)% of \(6000\)

\(= (\frac{45}{100} \times 6000) = 2700.\)

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46.

If \(A = x\)% of \(y\) and \(B = y\)% of \(x\), then which of the following is true?

A.A is smaller than B.
B.A is greater than B
C.Relationship between A and B cannot be determined.
D.None of these

Answer: D

\(x\)% of \(y\) \(= (\frac{x}{100} \times y) = (\frac{y}{100} \times x) = y\)% of \(x\)

\(\therefore A = B\)

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47.

A grain dealer cheats to the extent of 10% while buying as well as selling by using false weights. His total profit percentage is :

A.20 %
B.22.22 %
C.23.23 %
D.25 %

Answer: B

The retailer buys 110 gram in Rs 100 because of 10 % cheating so cost price = 1 gram = Rs \(\frac{100}{110}\) = Rs 0.909 and retailer sells 90 gram in Rs 100

and hence selling price = Rs 100 / 90 = Rs 1.111

Profit % \(= \frac{1.111-0.909}{0.909} = 22.22\)

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48.

Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56 % of the sum of their marks. The marks obtained by them are:

A.39, 30
B.41, 32
C.42, 33
D.43, 34

Answer: C

Their marks be \((x + 9)\) and \(x\)

Then, \(x + 9 = \frac{56}{100}(x + 9 + x)\)

\(\Rightarrow 25(x + 9) = 14(2x + 9) \)

\(\Rightarrow 3x = 99 \)

\(\Rightarrow x = 33\)

So, their marks are 42 and 33.

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49.

Two tailors \(X\) and \(Y\) are paid a total of \(Rs. 550\) per week by their employer. If \(X\) is paid \(120\) % of the sum paid to \(Y\), how much is \(Y\) paid per week?

A.Rs. 200
B.Rs. 250
C.Rs. 300

Answer: B

The sum paid to \(Y\) per week be \(Rs. Z.\)

Then, \(Z + 120\) % of \(Z = 550.\)

\(\Rightarrow Z + \frac{120}{100}Z =550\)

\(\Rightarrow \frac{11}{5}Z = 550\)

\(\Rightarrow Z = (\frac{550 \times 5}{11}) = 250.\)

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50.

In a certain school, 20 % of students are below 8 years of age. The number of students above 8 years of age is\(\frac{2}{3}\) of the number of students of 8 years of age which is 48. What is the total number of students in the school?

A.72
B.80
C.120
D.100

Answer: D

Let the number of students be \(x\).

Then, Number of students above 8 years of age \(= (100 -20)\)% of \(x = 80\)% of \(x\)

\(\therefore 80\)% of \(x = 40 + \frac{2}{3} \) of 48

\(\Rightarrow \frac{80}{100}x = 80\)

\(\Rightarrow x = 100.\)

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