Question

Smitha's collection of 113 greeting cards include a mix of birthday cards, new year cards, Diwali cards, Christmas cards, and a marriage anniversary card. The number of birthday cards is equal to the sum of all the others except the marriage anniversary card. The number of new year's cards is double the number of Diwali cards. Which in turn is double the number of Christmas cards. Then the ratio of the birthday cards to the Christmas cards in her collection is

1. 7 ∶ 1
2. 7 ∶ 2
3. 5 ∶ 2
4. 8 ∶ 3

Answer 1

Correct Answer - Option 1 : 7 ∶ 1

Given:

Total number of cards is 113

The number of Birthday cards is equal to the sum of all the others except the marriage anniversary card.

The number of New year's cards is double the number of Diwali cards.

The number of Diwali's cards is double the number of Christmas cards.

Calculation:

Let the number of Christmas card be x

⇒ Total number of Diwali cards = 2x

⇒ Total number of New year's cards  = 4x

Total number of Birthday cards,

⇒ x + 2x + 4x

⇒ 7x

According to the question,

⇒ Birthday cards ∶ Christmas card = 7x ∶ x

⇒ Birthday cards ∶ Christmas card = 7 ∶ 1

∴ The ratio is 7 ∶ 1.