A group of girls went for shopping. The average number of items purchased by the first half of the girls is equal to the average amount spent by the other half and the average amount spent by the first half of the girls is equal to the average number of items purchased by the other half. If the total amount spent by all the girls is Rs. 234, then what can be the total number of items purchased by the girls in the first half, if the average amount spent by the girls in each half is an integer? (The average amount spent by the girls in the first half is more than Rs. 10).
Explanation:
Let the number of items purchased and the average amount spent by the first half are 'a' and 'b' respectively.
Then, the total amount spent by all the girls is 2ab. Now, if 2ab = 234 then ab = 117.
Hence a can be a factor of 117 i.e. 1, 3, 9, 13, 39 and 117. Because b is more than 10, a must be 1, 3 or 9.
Hence, option (c).
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