{"id":212243,"date":"2025-02-17T10:03:31","date_gmt":"2025-02-17T04:33:31","guid":{"rendered":"https:\/\/cracku.in\/blog\/?p=212243"},"modified":"2025-02-20T17:41:43","modified_gmt":"2025-02-20T12:11:43","slug":"cat-percentages-questions-pdf","status":"publish","type":"post","link":"https:\/\/cracku.in\/blog\/cat-percentages-questions-pdf\/","title":{"rendered":"CAT Percentages Questions PDF [Important With Solutions]"},"content":{"rendered":"
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Percentages hold significant importance in the Quantitative Ability (QA) section of CAT. It is a relatively straightforward topic, and it is crucial not to overlook it. Every year, 1-2 questions are dedicated to percentages in the CAT exam. You can refer to the CAT Previous year’s papers<\/strong><\/a> for percentage-based questions. It is advisable to practice an ample number of CAT Percentage questions to ensure you don’t miss out on the easy questions from this topic. This article focuses on essential Percentage Questions for CAT Quants, providing a valuable source for practice. If you wish to practice these questions, feel free to download the CAT Percentages Questions PDF provided below, completely free of charge.<\/p>\n<\/div>\n<\/div>\n<\/div>\n

Download Percentage Questions for CAT<\/a><\/p>\n

CAT Online Coaching<\/a><\/p>\n

Question 1:\u00a0<\/b>In a group of people, 28% of the members are young while the rest are old. If 65% of the members are literates, and 25% of the literates are young, then the percentage of old people among the illiterates is nearest to<\/p>\n

a)\u00a062<\/p>\n

b)\u00a055<\/p>\n

c)\u00a059<\/p>\n

d)\u00a066<\/p>\n

1)\u00a0Answer\u00a0(D)<\/strong><\/p>\n

View Video Solution<\/a><\/p>\n

Solution:<\/b><\/p>\n

Let ‘x’ be the strength of group G. Based on the information, $0.65x$ constitutes of literate people {the rest $0.35x$ =\u00a0illiterate}
\nOf this $0.65x$, 75% are old people =(0.75)0.65x old literates. The total number of old people in group G is $0.72x$ {72% of the total}. Thus, the total number of old people who are illiterate = $0.72x-0.4875x\\ =\\ 0.2325x$. This is $\\frac{0.2325x}{0.35x}\\times\\ 100\\ \\approx\\ \\ 66\\%$ of the total number of illiterates. Hence, Option D is the correct answer.<\/p>\n

Question 2:\u00a0<\/b>Anil buys 12 toys and labels each with the same selling price. He sells 8 toys initially\u00a0at 20% discount on the labeled price. Then he sells the remaining 4 toys at an\u00a0additional 25% discount on the discounted price. Thus, he gets a total of Rs 2112, and\u00a0makes a 10% profit. With no discounts, his percentage of profit would have been<\/p>\n

a)\u00a050<\/p>\n

b)\u00a060<\/p>\n

c)\u00a054<\/p>\n

d)\u00a055<\/p>\n

2)\u00a0Answer\u00a0(A)<\/strong><\/p>\n

View Video Solution<\/a><\/p>\n

Solution:<\/b><\/p>\n

Let the CP of the each toy be “x”. CP of 12 toys will be “12x”. Now the shopkeeper made a 10% profit on CP. This means that<\/p>\n

12x(1.1)= 2112 or x=160 . Hence the CP of each toy is \u20b9160.<\/p>\n

Now let the SP of each toy be “m”. Now he sold 8 toys at 20% discount. This means that 8m(0.8) or 6.4m<\/p>\n

He sold 4 toys at an additional 25% discount. 4m(0.8)(0.75)=2.4m\u00a0 Now 6.4m+2.4m=8.8m=2112 or m=240<\/p>\n

Hence CP= 160 and SP=240. Hence profit percentage is 50%.<\/p>\n

Question 3:\u00a0<\/b>Raj invested \u20b9 10000 in a fund. At the end of first year, he incurred a loss but his balance was more than \u20b9 5000. This balance, when invested for another year, grew and the percentage of growth in the second year was five times the percentage of loss in the first year. If the gain of Raj from the initial investment over the two year period is 35%, then the percentage of loss in the first year is<\/p>\n

a)\u00a05<\/p>\n

b)\u00a015<\/p>\n

c)\u00a017<\/p>\n

d)\u00a010<\/p>\n

3)\u00a0Answer\u00a0(D)<\/strong><\/p>\n

View Video Solution<\/a><\/p>\n

Solution:<\/b><\/p>\n

Raj invested Rs 10000 in the first year. Assuming the loss he faced was x%.<\/p>\n

The amount after 1 year is 10,000*(1 – x\/100). = 10000 – 100*x.<\/p>\n

Given the balance was greater than Rs 5000 and hence x < 50 percent.<\/p>\n

When Raj invested this amount in the second year he earned a profit which is five times that of the first-year percentage.<\/p>\n

Hence the amount after the second year is : (10000 – 100x)(1+$\\frac{\\left(5\\cdot x\\right)}{100}$).<\/p>\n

Raj gained a total of 35 percent over the period of two years and hence the 35 percent is Rs 3500.<\/p>\n

Hence the final amount is Rs 13,500.<\/p>\n

(10000 – 100x)(1+$\\frac{\\left(5\\cdot x\\right)}{100}$) = 13,500<\/p>\n

$\\left(100+5\\cdot x\\right)\\cdot\\left(100\\ -\\ x\\right)\\ =\\ 13500$<\/p>\n

10000 – 100*x +500*x – 5*$x^2$ = 13500.<\/p>\n

$5x^2-400x+3500\\ =\\ 0$<\/p>\n

Solving the equation the roots are :<\/p>\n

x = 10, x = 70.<\/p>\n

Since x < 50, x = 10 percent.<\/p>\n

Question 4:\u00a0<\/b>Meena scores 40% in an examination and after review, even though her score is increased by 50%, she fails by 35 marks. If her post-review score is increased by 20%, she will have 7 marks more than the passing score. The percentage score needed for passing the examination is<\/p>\n

a)\u00a060<\/p>\n

b)\u00a080<\/p>\n

c)\u00a070<\/p>\n

d)\u00a075<\/p>\n

4)\u00a0Answer\u00a0(C)<\/strong><\/p>\n

View Video Solution<\/a><\/p>\n

Solution:<\/b><\/p>\n

Assuming the maximum marks =100a, then Meena got 40a<\/p>\n

After increasing her score by 50%, she will get 40a(1+50\/100)=60a<\/p>\n

Passing score = 60a+35<\/p>\n

Post review score after 20% increase = 60a*1.2=72a<\/p>\n

=>Hence, 60a+35+7=72a<\/p>\n

=>12a=42\u00a0 \u00a0=>a=3.5<\/p>\n

=> maximum marks = 350 and passing marks = 210+35=245<\/p>\n

=> Passing percentage = 245*100\/350 = 70<\/p>\n

Question 5:\u00a0<\/b>After allowing a discount of 11.11%, a trader still makes a gain of 14.28%. At how many percentage above the cost price does he mark on his goods?<\/p>\n

a)\u00a028.56%<\/p>\n

b)\u00a035%<\/p>\n

c)\u00a022.22%<\/p>\n

d)\u00a0None of these<\/p>\n

5)\u00a0Answer\u00a0(A)<\/strong><\/p>\n

View Video Solution<\/a><\/p>\n

Solution:<\/b><\/p>\n

Let’s say cost price is 100
\ngain = 14.28
\nselling price = 114.28
\nMarked price = x(say)
\nSo $x- \\frac{11.11x}{100} = \\frac{8x}{9} = 114.28$
\nOr $x = 128.52$
\nSo marked price is 28.52% more than cost price.<\/p>\n

Checkout: CAT Free Practice Questions and Videos<\/strong><\/a><\/em><\/p>\n

Question 6:\u00a0<\/b>The income of Amala is 20% more than that of Bimala and 20% less than that of Kamala. If Kamala’s income goes down by 4% and Bimala’s goes up by 10%, then the percentage by which Kamala’s income would exceed Bimala’s is nearest to<\/p>\n

a)\u00a031<\/p>\n

b)\u00a029<\/p>\n

c)\u00a028<\/p>\n

d)\u00a032<\/p>\n

6)\u00a0Answer\u00a0(A)<\/strong><\/p>\n

View Video Solution<\/a><\/p>\n

Solution:<\/b><\/p>\n

Assuming the income of Bimla = 100a, then the income of Amala will be 120a.<\/p>\n

And the income of Kamala will be 120a*100\/80=150a<\/p>\n

If Kamala’s income goes down by 4%, then new income of Kamala = 150a-150a(4\/100) = 150a-6a=144a<\/p>\n

If Bimla’s income goes up by 10 percent, her new income will be 100a+100a(10\/100)=110a<\/p>\n

=> Hence the Kamala income will exceed Bimla income by (144a-110a)*100\/110a=31<\/p>\n

Question 7:\u00a0<\/b>In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 95% of the products of M3 are not defective. What is the percentage of defective in the stockpile?<\/p>\n

a)\u00a03%<\/p>\n

b)\u00a05%<\/p>\n

c)\u00a02.5%<\/p>\n

d)\u00a04%<\/p>\n

7)\u00a0Answer\u00a0(A)<\/strong><\/p>\n

View Video Solution<\/a><\/p>\n

Solution:<\/b><\/p>\n

Let’s say total products maufactured by M1, M2 and M3 are 100.<\/p>\n

So M1 produced 40, M2 produced 30 and M3 produced 30<\/p>\n

Defective pieces for M1 = $\\frac{120}{100}$<\/p>\n

Defective pieces for M2 = $\\frac{30}{100}$<\/p>\n

Defective pieces for M3 = $\\frac{150}{100}$<\/p>\n

So total defective pieces are $\\frac{150+30+120}{100}$ = $\\frac{300}{100}$ = 3% of total products.<\/p>\n

Question 8:\u00a0<\/b>I sold two watches for Rs. 300 each, one at the loss of 10% and the other at the profit of 10%. What is the percentage of loss(-) or profit(+) that resulted from the transaction?<\/p>\n

a)\u00a0(+)10<\/p>\n

b)\u00a0(-)1<\/p>\n

c)\u00a0(+)1<\/p>\n

d)\u00a0(-)10<\/p>\n

8)\u00a0Answer\u00a0(B)<\/strong><\/p>\n

View Video Solution<\/a><\/p>\n

Solution:<\/b><\/p>\n

Selling price of first watch = 300
\nProfit = 10%
\ncost price = $\\frac{300}{1.1}$
\nSelling price of second watch = 300
\nLoss = 10%
\ncost price = $\\frac{300}{0.9}$<\/p>\n

Total selling price of transaction= 600
\nTotal cost price of transaction = $300(\\frac{10}{11} + \\frac{10}{9}) = 600 (\\frac{100}{99})$
\nLoss = $600 (\\frac{100}{99} – 1)$
\n%loss = $(600 (\\frac{100}{99} – 1)) \\div (600(\\frac{100}{99})) \\times 100 = 1$<\/p>\n

Question 9:\u00a0<\/b>In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 95% of the products of M3 are not defective. What is the percentage of defective in the stockpile?<\/p>\n

a)\u00a03%<\/p>\n

b)\u00a05%<\/p>\n

c)\u00a02.5%<\/p>\n

d)\u00a04%<\/p>\n

9)\u00a0Answer\u00a0(A)<\/strong><\/p>\n

View Video Solution<\/a><\/p>\n

Solution:<\/b><\/p>\n

Let’s say total products maufactured by M1, M2 and M3 are 100.<\/p>\n

So M1 produced 40, M2 produced 30 and M3 produced 30<\/p>\n

Defective pieces for M1 = $\\frac{120}{100}$<\/p>\n

Defective pieces for M2 = $\\frac{30}{100}$<\/p>\n

Defective pieces for M3 = $\\frac{150}{100}$<\/p>\n

So total defective pieces are $\\frac{150+30+120}{100}$ = $\\frac{300}{100}$ = 3% of total products.<\/p>\n

Question 10:\u00a0<\/b>Instead of a metre scale, a cloth merchant uses a faulty 120 cm scale while buying, but uses a faulty\u00a080 cm scale while selling the same cloth. If he offers a discount of 20%, what is his overall profit percentage?<\/p>\n

a)\u00a020%<\/p>\n

b)\u00a025%<\/p>\n

c)\u00a040%<\/p>\n

d)\u00a015%<\/p>\n

10)\u00a0Answer\u00a0(A)<\/strong><\/p>\n

View Video Solution<\/a><\/p>\n

Solution:<\/b><\/p>\n

Let’s say the cost of the cloth is x rs per metre. Because of the faulty meter, he is paying x for 120 cms when buying.<\/p>\n

So cost of 100 cms = 100x\/120.<\/p>\n

He is selling 80 cms for x, so selling price of 100cms of cloth\u00a0is 100x\/80.<\/p>\n

discount = 20%<\/p>\n

so the effective\u00a0selling price is .8*100x\/80= x<\/p>\n

profit = SP-CP= x – 100x\/120 = x\/6<\/p>\n

Profit % = x\/6 divided by 100x\/120 = 20%<\/p>\n

CAT 2023 Preparation Videos<\/span><\/h2>\n