{"id":5770,"date":"2026-10-15T13:21:35","date_gmt":"2026-10-15T07:51:35","guid":{"rendered":"https:\/\/www.catmock.com\/blog\/?p=5770"},"modified":"2026-10-15T13:21:36","modified_gmt":"2026-10-15T07:51:36","slug":"most-important-cat-averages-questions","status":"publish","type":"post","link":"https:\/\/www.catmock.com\/blog\/most-important-cat-averages-questions\/","title":{"rendered":"Most Important CAT Averages Questions: Types, Formulas and Solved Examples"},"content":{"rendered":"\n

Averages look like the easiest chapter in CAT Quant. Many aspirants still lose marks here because they average two averages, miss a count, or use the wrong speed formula. The most important CAT averages questions are not hard. They are slippery, and a small slip costs a question you could have solved in a minute.<\/p>\n\n\n\n

This guide covers the question types that matter, the formulas behind them, and solved examples. You will also find a free CAT averages questions PDF<\/strong> with 35 questions and solutions, and a formula sheet.<\/p>\n\n\n

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\n\t\t\t\t\tCAT Previous year Averages Questions with Solutions <\/strong><\/span>\n\t\t\t\t<\/div>\n\t\t\t<\/a>\n\t\t<\/div><\/div>\n\n\n

Why CAT Averages Questions Matter<\/h3>\n\n\n\n

CAT 2026 is scheduled for 29 November 2026<\/strong>, so check the official notification at iimcat.ac.in<\/mark><\/a> for any change. The expected pattern is 68 questions in 120 minutes, with 40 minutes per section. The Quantitative Aptitude section is expected to have 22 questions, and arithmetic is commonly reported to make up roughly half of it.<\/p>\n\n\n\n

Averages work as a foundation topic. They appear directly, and they sit inside weighted averages, mixtures and alligation, data interpretation sets, and time-speed-distance. A student who is solid on averages is faster on all of these.<\/p>\n\n\n\n

CAT Averages Questions at a Glance<\/h3>\n\n\n\n
Question type<\/th>Core idea<\/th>Difficulty<\/th><\/tr><\/thead>
Basic average and series<\/td>Sum = Average \u00d7 Number of terms<\/td>Easy<\/td><\/tr>
Weighted \/ combined average<\/td>Weight each group by its size<\/td>Easy\u2013Moderate<\/td><\/tr>
Adding or removing an item<\/td>Track totals, not averages<\/td>Moderate<\/td><\/tr>
Replacement<\/td>Change in total = n \u00d7 change in average<\/td>Moderate<\/td><\/tr>
Average speed<\/td>Total distance \u00f7 total time<\/td>Moderate<\/td><\/tr>
Min\/max with distinct integers<\/td>Push other values to extremes<\/td>Hard<\/td><\/tr>
Alligation-based averages<\/td>Ratio = distance of the mean from each end<\/td>Moderate\u2013Hard<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

The Formulas You Must Know for CAT Averages Questions<\/h3>\n\n\n\n

Remember one rule above all: work with totals.<\/strong> Convert every average into a sum, do the arithmetic, then convert back.<\/p>\n\n\n\n

Concept<\/th>Formula<\/th><\/tr><\/thead>
Average<\/td>Sum \u00f7 Number of items<\/td><\/tr>
First n natural numbers<\/td>(n + 1) \/ 2<\/td><\/tr>
First n odd numbers<\/td>n<\/td><\/tr>
First n even numbers<\/td>n + 1<\/td><\/tr>
Equally spaced terms (AP)<\/td>(First + Last) \/ 2<\/td><\/tr>
Combined average of two groups<\/td>(n\u2081A\u2081 + n\u2082A\u2082) \/ (n\u2081 + n\u2082)<\/td><\/tr>
New item added to n items, average changes by d<\/td>New item = Old average + (n + 1) \u00d7 d<\/td><\/tr>
One item replaced in a group of n<\/td>New item = Old item + n \u00d7 change in average<\/td><\/tr>
Average speed, equal distances<\/td>2xy \/ (x + y)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n
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\n\t\t\t\t\tCAT Averages Formula Sheet pdf<\/strong><\/span>\n\t\t\t\t<\/div>\n\t\t\t<\/a>\n\t\t<\/div><\/div>\n\n\n

Most Important CAT Averages Questions with Solutions<\/h3>\n\n\n\n

1. Weighted average questions<\/h4>\n\n\n\n

Many \u201caverage of averages\u201d questions test whether you weight by group size.<\/p>\n\n\n\n

Question:<\/strong> 30 students average 60 marks and 20 students average 75. What is the average of all 50?<\/p>\n\n\n\n

Solution:<\/strong> Total = 30 \u00d7 60 + 20 \u00d7 75 = 1800 + 1500 = 3300. Average = 3300 \/ 50 = 66<\/strong>.<\/p>\n\n\n\n

If you had averaged 60 and 75 directly, you would get 67.5, which is wrong. The larger group is the 60-mark group, so the answer sits closer to 60.<\/p>\n\n\n\n

2. Replacement questions<\/h4>\n\n\n\n

Question:<\/strong> The average weight of 8 people rises by 2.5 kg when a 65 kg person is replaced. What is the new person\u2019s weight?<\/p>\n\n\n\n

Solution:<\/strong> The total rises by 8 \u00d7 2.5 = 20 kg. New weight = 65 + 20 = 85 kg<\/strong>.<\/p>\n\n\n\n

3. Batsman average questions<\/h4>\n\n\n\n

Question:<\/strong> A batsman scores 85 in his 17th innings and his average rises by 3. What is his average now?<\/p>\n\n\n\n

Solution:<\/strong> New average = 85 \u2212 (16 \u00d7 3) = 37<\/strong>. Check: the old average is 34, so 34 \u00d7 16 = 544. Then 544 + 85 = 629, and 629 \/ 17 = 37.<\/p>\n\n\n\n

4. Average speed questions<\/h4>\n\n\n\n

This is where the simple mean fails.<\/p>\n\n\n\n

Question:<\/strong> A car travels uphill at 60 km\/h and returns at 40 km\/h over the same road. What is its average speed?<\/p>\n\n\n\n

Solution:<\/strong> For equal distances, average speed = 2 \u00d7 60 \u00d7 40 \/ (60 + 40) = 48 km\/h<\/strong>. It is not 50 km\/h, because the car spends more time at the slower speed.<\/p>\n\n\n\n

Use the simple mean only when the times<\/strong> are equal.<\/p>\n\n\n\n

5. Maximum and minimum value questions<\/h4>\n\n\n\n

These questions test reasoning more than calculation.<\/p>\n\n\n\n

Question:<\/strong> The average of 5 distinct positive integers is 20. What is the largest value the biggest integer can take?<\/p>\n\n\n\n

Solution:<\/strong> The total is 100. To maximise one number, make the other four as small as possible: 1, 2, 3 and 4, which sum to 10. The largest is 100 \u2212 10 = 90<\/strong>.<\/p>\n\n\n\n

6. Alligation-based average questions<\/h4>\n\n\n\n

Question:<\/strong> A class averages 62 marks. Boys average 60 and girls average 65. What is the ratio of boys to girls?<\/p>\n\n\n\n

Solution:<\/strong> Boys : Girls = (65 \u2212 62) : (62 \u2212 60) = 3 : 2<\/strong>. The class mean is closer to the boys\u2019 mean, so there are more boys.<\/p>\n\n\n\n

This links averages to mixtures and alligation for CAT<\/mark><\/a>.<\/p>\n\n\n\n

CAT Averages Questions PDF: Free Practice Set<\/h3>\n\n\n\n

To practise under exam conditions, download these two files:<\/p>\n\n\n\n