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# The prices of a scooter and a cycle are in the ratio $9:5$. If scooter costs Rs.4200 more than the cycle, the price of the cycle is:(A) Rs.5250 (B) Rs.5200 (C) Rs.5000 (D) Rs.4800

Last updated date: 21st Jul 2024
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Hint: Assume the cost of scooter and cycle to be 9x and 5x respectively. Find out the difference between them and satisfy the condition given in the question.

According to the question, the prices of scooter and cycle are in the ratio $9:5$. Let the price of a scooter is $9x$ and that of a cycle is $5x$.
Given, the cost of scooter is Rs.4200 more than that of cycle. So, we have:
$\Rightarrow 9x - 5x = 4200, \\ \Rightarrow 4x = 4200, \\ \Rightarrow x = 1050 \\$
The value of $x$ is $1050$.
Then, the cost of the cycle is $5x = 5 \times 1050 = 5250$.

The cost of cycle is Rs.5250. (A) is the correct option.

Note: We can solve the question using the ratio and proportion method also.
The costs of scooter and cycle are in the ratio $9:5$. Thus, the difference between their costs is 4 ratios. And the difference between their costs is already given in question and it is Rs.4200.
So, 4 ratio is equivalent to 4200.
Hence, 1 ratio is equivalent to $\dfrac{{4200}}{4} = 1050$
And the cost of a cycle is 5 ratios. So, the cost of cycle is $5 \times 1050 = 5250$