Read the following information carefully and answer the questions below it.…
2022
Read the following information carefully and answer the questions below it.
Rashmi is very fond of collecting greeting cards. Her collection of 211 cards has a good mix of Birthday cards, New Year cards, Deepawali cards, Christmas cards and even a Marriage anniversary card. The number of Birthday cards is equal to the sum of the others except the Marriage anniversary cards. The number of New Year card is double of Deepawali cards which in turn is double of Christmas cards.
Ques: The number of Deepawali card is
- A.
30
- B.
25
- C.
36
- D.
40
Attempted by 4 students.
Show answer & explanation
Correct answer: A
Concept: In a part-whole ratio problem, express every category as a multiple of the smallest share using the given ratios, then use the total (and any category defined as a sum of others) to solve for that share.
Let the number of Christmas cards = C. Since New Year cards are double Deepawali cards, and Deepawali cards are double Christmas cards, Deepawali cards = 2C and New Year cards = 2 x 2C = 4C.
The phrase "even a Marriage anniversary card" (singular) tells us there is exactly one such card, so Marriage anniversary cards = 1.
Birthday cards equal the sum of all categories except the Marriage anniversary card: Birthday = New Year + Deepawali + Christmas = 4C + 2C + C = 7C.
The total collection is 211 cards, so Birthday + New Year + Deepawali + Christmas + Marriage anniversary = 211, i.e. 7C + 4C + 2C + C + 1 = 211, which gives 14C + 1 = 211.
Solving: 14C = 210, so C = 15.
Deepawali cards = 2C = 2 x 15 = 30.
Cross-check: Substituting C = 15 back: Christmas = 15, Deepawali = 30, New Year = 60, Marriage anniversary = 1, and Birthday = 60 + 30 + 15 = 105. All five categories sum to 105 + 60 + 30 + 15 + 1 = 211, matching the given total exactly, and Birthday (105) equals New Year + Deepawali + Christmas (60 + 30 + 15 = 105) as required.
Answer: So the number of Deepawali cards is 30.