Puzzle on Profit and Loss - My friend collects antique stamps...

Question:  My friend collects antique stamps. She purchased two, but found that she needed to raise money urgently. So she sold them for Rs. 8000 each. On one she made 20% and on the other she lost 20%.

How much did she gain or lose in the entire transaction?


Answer:
She lost Rs 666.67

Solution:
Consider the first stamp. She mades 20% on it after selling it for Rs 8000.

So the original price of first stamp is
= (8000 * 100) / 80
= Rs 6666.67

Similarly, consider second stamp. She lost 20% on it after selling it for Rs 8000

So the original price of second stamp is
= (8000 * 100) / 80
= Rs 10000

Total buying price of two stamps
= Rs 6666.67 + Rs 10000
= Rs 16666.67

Total selling price of two stamps
= Rs 8000 + Rs 8000
= Rs 16000

Hence, she lost Rs 666.67

Puzzle on Logical Reasoning - At the Party there were 9 men and children......

Question: At the Party:

• There were 9 men and children.
• There were 2 more women than children.
• The number of different man-woman couples possible was 24. Note that if there were 7 men and 5 women, then there would have been 35 man-woman couples possible.
•  Also, of the three groups - men, women and children - at the party:
• There were 4 of one group.
• There were 6 of one group.
• There were 8 of one group.

Exactly one of the above 6 statements is false.

Can you tell which one is false? Also, how many men, women and children are there at the party?

Answer:    Statement (4) is false. There are 3 men, 8 women and 6 children.

Solution: 

Assume that Statements (4), (5) and (6) are all true. Then, Statement (1) is false. But then Statement (2) and (3) both can not be true. Thus, contradictory to the fact that exactly one statement is false. So Statement (4) or Statement (5) or Statement (6) is false. Also, Statements (1), (2) and (3) all are true. From (1) and (2), there are 11 men and women. Then from (3), there are 2 possible cases - either there are 8 men and 3 women or there are 3 men and 8 women. If there are 8 men and 3 women, then there is 1 child. Then Statements (4) and (5) both are false, which is not possible. Hence, there are 3 men, 8 women and 6 children. Statement (4) is false.