Dittee has 10 purses and each of which having an average of 25 lipsticks in each purse. Further, it is known that each purse has a minimum of 8 lipsticks and none of the purse has identical number of lipsticks.
Determine that what can be the maximum number of lipsticks that Dittee shall have in any of her purse?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 142
The average fixes the total number of lipsticks. One purse holds the most when the other nine hold as few as the conditions allow: at least 8 each, and no two equal, so 8, 9, 10, …, 16.
Total lipsticks \(=10\times25=250\)
Least for the other nine purses \(=8+9+10+\dots+16=\frac{9\times(8+16)}{2}=108\)
Largest number in one purse \(=250-108=142\)