CAT 2025 Slot 2 · Quant · Question 3

CAT 2025 Slot 2 previous year question on Averages, Mixture and Alligation, with the answer and a step-by-step solution.

Averages, Mixture and AlligationArithmeticType in the answer (TITA)Medium
The average number of copies of a book sold per day by a shopkeeper is 60 in the initial seven days and 63 in the initial eight days, after the book launch. On the ninth day, she sells 11 copies less than the eighth day, and the average number of copies sold per day from second day to ninth day becomes 66. The number of copies sold on the first day of the book launch is
Answer & solution

Answer: 49

Seven days at an average of 60 give 7\times 60=420 copies over days 1 to 7.

Eight days at an average of 63 give 8\times 63=504 copies over days 1 to 8.

Day 8 is the difference: 504-420=84 copies.

Day 9 is 11 fewer: 84-11=73 copies.

Days 1 to 9 therefore total 504+73=577 copies.

Days 2 to 9 total 8\times 66=528 copies.

Day 1 is what is left over: 577-528=49 copies.

Shortcut. A jump in a running average tells you the new term at once: going from an average of 60 over 7 days to 63 over 8 days means day 8 sits 8\times 63-7\times 60 above nothing, i.e. the new average plus 7 times the rise, 63+7\times 3=84. The same trick ends the question: day 1 is the overlap of the two totals.

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