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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.

Complete step-by-step answer:

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 $5 \times 1050 = 5250$