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Ratio and average questions look different on the surface but use the same core idea: comparing parts to a whole.
A ratio a : b compares two quantities of the same kind. To divide a total T in ratio a : b, the two parts are (a/(a+b)) × T and (b/(a+b)) × T.
Four quantities a, b, c, d are in proportion if a/b = c/d, written a : b :: c : d. Product of extremes = product of means → a × d = b × c.
Average = Sum of observations ÷ Number of observations.
Combined average of two groups: (n₁ × A₁ + n₂ × A₂) / (n₁ + n₂), where n is the count and A is the average of each group.
UdaanPath runs a ₹4,500 top-scorer reward pool for a mock test, to be split between the top two students A and B in the ratio 4 : 5.
A's share = (4/9) × 4500 = ₹2,000. B's share = (5/9) × 4500 = ₹2,500.
The average score of 30 students in an UdaanPath SSC mock test is 62. A 31st student joins and scores 93. Find the new average.
Total score of 30 students = 30 × 62 = 1860. New total = 1860 + 93 = 1953. New average = 1953/31 ≈ 63 marks.
An UdaanPath Railway batch of 20 students has an average mock-test score of 68, and a Banking batch of 30 students has an average of 72. Find the combined average across both batches.
Combined average = (20×68 + 30×72) / 50 = (1360 + 2160) / 50 = 3520/50 = 70.4.
When a value is added/removed from a group, don't just adjust the average by that value directly — always go back to the total sum first, then recompute.
1. Divide ₹6,000 between A and B in the ratio 2 : 3. What is B's share?
2. If 4 : 7 = x : 35, find x.
3. The average of 4 numbers is 15. If a fifth number, 25, is added, what is the new average?
4. An UdaanPath SSC batch of 25 students has an average mock-test score of 70. An additional Railway batch of 25 students has an average of 60. What is the combined average?