There are 100 wine glasses. I offered my servant 3 paise for every glass he…
2024
There are 100 wine glasses. I offered my servant 3 paise for every glass he delivered safely, but he would forfeit 9 paise for every glass broken. At the end of the day, he received Rs 2.40. How many glasses did he break?
- A.
3
- B.
5
- C.
6
- D.
8
Show answer & explanation
Correct answer: B
Concept: In a wage-and-penalty problem, the net amount paid equals (reward rate x number of successes) minus (penalty rate x number of failures), where successes + failures equal the total items handled. Setting up one linear equation in the unknown count of failures solves the problem.
Let x be the number of glasses broken. Then the number of glasses delivered safely is 100 - x.
Convert the amount received to paise: Rs 2.40 = 240 paise.
Write the net payment equation: 3 x (100 - x) - 9 x x = 240.
Simplify: 300 - 3x - 9x = 240, so 300 - 12x = 240.
Solve for x: 12x = 60, so x = 5.
Cross-check: with 95 glasses delivered safely and 5 broken, the payment is (95 x 3) - (5 x 9) = 285 - 45 = 240 paise, which is exactly Rs 2.40 as stated.