Question

Ram ordered for 6 black toys and some brown toys. The price of
a black toy is 5/2 times that of a brown toy. But while making the
bill the clerk interchanged the numbers of black and brown toys
due to which there was 45% increase in the amount of the bill.
Find the number of brown toys.
a) 20 b) 15 c) 17 d) 18​

Answer 1

The number of brown toys is 15.

Step-by-step explanation:

Ram ordered for 6 black toys and some brown toys.

Let the price of brown toy = Rs. x

Let the number of brown toys = y

Total price of brown toys = Rs. xy

The price of a black toy is $\frac{5}{2}$ times that of a brown toy.

Price of a black toy = Rs. $\frac{5x}{2}$

Total price of black toy = Rs. $6\times \frac{5x}{2}$ = Rs. 15x

Total price of black and brown toys = xy + 15x

While making the bill the clerk interchanged the numbers of black and brown toys due to which there was 45% increase in the amount of bill.

Total price of black and brown toys after interchange = 6x + $\frac{5xy}{2}$

$6x + \frac{5xy}{2} = \frac{145}{100}(xy + 15x)\\=> 6x + \frac{5xy}{2} = \frac{29}{20}(xy+15x)\\=> \frac{12x + 5xy}{2} = \frac{29xy + 435x}{20}\\=> {12x+5xy} = \frac{29xy + 435x}{10}$

=> 120x + 50xy = 29xy + 435x

=> 435x - 120x = 50xy - 29xy

=> 315x = 21xy

=> y = $\frac{315}{21}$ = 15

Hence, the number of brown toys is 15.