Bunuel wrote:
Ankur bought 5 Pizzas, 7 Samosas and 4 ice-creams. Sanjeev bought 6 Pizzas, 14 Samosas and 8 Ice creams for an amount which was 50% more than what Ankur paid. What percentage of the total amount spent by Ankur was spent on the Pizzas?
(A) 37.5%
(B) 45%
(C) 50%
(D) 56.5%
(E) 62.5%
Solution:
Let us consider P -> Cost per pizza, S -> Cost per samosa, I -> Cost per ice-cream.
Ankur has bought 5 Pizzas, 7 Samosas and 4 Ice-creams. Ankur(A) has spent:
A = 5P + 7S + 4I --> (1)Similarly, Sanjeev bought 6 Pizzas, 14 Samosas and 8 Ice creams. Sanjeev(J) has spent:
J = 6P + 14S + 8I --> (2)Given, Sanjeev has spent 50% more than Ankur.
(2) = 150% of (1) --> (3)
Therefore, we from (3), we have
\(6P + 14S + 8I = 1.5 * (5P + 7S + 4I)\)
Simplifying this equation will lead us to the solution:
\(6P + 14S + 8I = 1.5 * (5P + 7S + 4I)\)
Expanding Right hand side of the equation:
\(6P + 14S + 8I = 7.5P + 10.5S + 6I\)
Further simplification by moving the like terms to the same side.
\(3.5S + 2I = 1.5P\)
Now, multiplying both sides with 2, results in:
3P = 7S + 4I --> (4)Now, we need to calculate the percentage of the total amount Ankur has spent on Pizzas.
This can be given by \(\frac{Cost of 5P}{(Cost of 5P + Cost of 7S + Cost of 4I)}\) --> (5)
Now, from (4), we know that Cost of 7S + 4I = Cost of 3P
Subsituting this in (5), we get,
Percent of total amount spent on Pizzas = \(\frac{5P}{(5P+3P)}*100\) = 62.5%
Correct Answer - 62.5% - Option E