# MATH MCQ – Percentages – 24 Question with full Solution

#### 01. The ratio 5:20 expressed as percent equals to

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Actually, it means 5 is what percent of 20, which can be calculated as, (5/20)*100 = 5 * 5 = 25

#### 02. A number is decreased by 10% and then increased by 10%. The number so obtained is 10 less than the original number. What was the original number?

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Let the original number be x. 👉 Final number obtained = 110% of (90% of x) =(110/100 * 90/100 * x) = (99/100)x. x-(99/100)x=10 => x =1000

#### 03. If A's height is 40% less than that of B, how much percent B's height is more than that of A?

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Excess of B's height over A's = [(40/(100 - 40)] x 100% = 66.66%

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#### 05. 11 1/9 % of 900?

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11 1/9 % = 1/9 👉 1/9 × 900 = 100

#### 06. A man spends 35% of his income on food, 25% on children's education and 80% of the remaining on house rent. What percent of his income he is left with?

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Then, income left = (100 -80)% of [100 - (35 + 25)] % of x 👉 20% of 40% of x 👉 20/100 * 40/100 * 100) % of x 👉 8 % of x.

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4*1/100 = 1/25.

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#### 10. In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 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?

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Let the number of students be x. 👉 Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x. 👉 80% of x = 48 + 2/3 of 48 👉 80/100x = 80 👉 x = 100.

#### 11. A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. The maximum marks are

Correct! Wrong!

Given that the student got 125 marks and still he failed by 40 marks👉 The minimum pass mark = 125 + 40 = 165👉 Given that minimum pass mark = 33% of the total mark👉 total mark =33/100 =165👉 total mark = 16500/33 = 500

#### 12. If A = x% of y and B = y% of x, then which of the following is true?

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x% of y = x/100 x y = y/100 x x/= y% of x A = B.

#### 13. A man spends 35% of his income on food, 25% on children's education and 80% of the remaining on house rent. What percent of his income he is left with?

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Let the total income be x. Then, income left = (100 -80)% of [100 - (35 + 25)] % of x = 20% of 40% of x = 20/100 * 40/100 * 100) % of x = 8 % of x.

#### 14. Half of 1 percent written as decimal is

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It will be 1/2(1%) 👉 1/2(1/100) 👉 1/200 👉 0.005

#### 15. 75 g of sugar solution has 30% sugar in it. Then, the quantity of sugar that should be added to the solution to make the quantity of the sugar 70% in the solution, is

Correct! Wrong!

Sugar in original solution = (75 x 30) / 100 = 22.5 g 👉 Let x g of sugar be mixed 👉 According to the question 👉 {(22.5 + p)/(75 + p)} x 100 = 70 👉 2250 + 100p = 75 × 70 + 70p 👉 2250 + 100p = 5250 + 70p 👉 30p = 5250 – 2250= 3000 👉 => p = 3000/30 = 100g

#### 16. A reduction of 10% in the price of wheat enables a man to buy 50 g of wheat more for a rupee. How much wheat could originally be had for a rupee?

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Original prices per kg= Rp/(100-p)y per kg 👉 {(1 x 10)/(100 – 10)0.05} = Rs. 20/9 /kg 👉 It means the man can buy 1 kg or 1000 gm in Rs 20/9 or he can buy 👉 (1000 x 9)/20 = 450g in one rupee.

#### 17. 2.09 can be expressed in terms of percentage as

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While calculation in terms of percentage we need to multiply by 100, so 2.09 * 100 = 209.

#### 18. Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate got

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Total number of votes polled = (1136 + 7636 + 11628) = 20400. So, Required percentage = 11628/20400 * 100 = 57%

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20*1/100 = 1/5

#### 21. A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:

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Suppose originally he had x apples.👉 Then, (100 - 40)% of x = 420. 👉 60/100 x x = 420 👉 x = 420 x 100/60 = 700.

#### 22. In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was :

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Total number of votes = 7500 👉 Given that 20% of Percentage votes were invalid 👉 => Valid votes = 80% 👉 Total valid votes = 7500*(80/100) 👉 1st candidate got 55% of the total valid votes. 👉 Hence the 2nd candidate should have got 45% of the total valid votes 👉 => Valid votes that 2nd candidate got = total valid votes x (45/100) 👉 7500*(80/100)*(45/100) = 2700

#### 23. 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:

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Let their marks be (x + 9) and x. 👉 Then, x + 9 = 56/100(x + 9 + x) 👉 25(x + 9) = 14(2x + 9) 👉 3x = 99 👉 x = 33 👉 So, their marks are 42 and 33.

#### 24. The price of sugar having gone down by 10%, a consumer can buy 5 kg more sugar for Rs 270. The difference between the original and reduced price per kg is

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Reduced price => Rp/100y per kg 👉 R = Rs 270 , p=10% ,y=5kg 👉 {(270×10)/(100×5)} = Rs. 5.4 👉 Original prices per kg= Rp/(100-p)y per kg 👉 {(270 x 10)/ (100 – 10)5} = 2700/450 = Rs. 6 👉 Difference will be = 6-5.4= Rs 0.6 = 60 paise

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