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The Taj Mahal Palace opened in Mumbai, in 1903. Alpha, Beta and Gamma three friends had a dinner at one of its famous restaurant. When the bill was received, Alpha paid 4/3 as much as Beta paid and Beta paid 1/4 as much as Gamma paid. What fraction of the bill did Beta pay?

The Taj Mahal Palace opened in Mumbai, in 1903. Alpha, Beta and Gamma three friends had a dinner at one of its famous restaurant. When the bill was received, Alpha paid 4/3 as much as Beta paid and Beta paid 1/4 as much as Gamma paid. What fraction of the bill did Beta pay? Correct Answer 3/19

Given ∶

Alpha paid 4/3 as much as Beta paid.

 Beta paid 1/4 as much as Gamma paid.

Formula Used∶

Simple concept of Ratio and Linear Equations.

Calculation∶

Let Beta paid Rs. x

So, Alpha paid Rs. 4x/3 and Gamma paid Rs. 4x

So, total bill paid is given by

(4x/3) + x + 4x =1

⇒ 4x + 3x + 12x = 3

⇒ 19x = 3

⇒ x = 3/19

∴ Beta paid 3/19 part of the bill.

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