Two numbers are in the ratio of 12 : 13. If their H.C.F. is 11, then the…
2023
Two numbers are in the ratio of 12 : 13. If their H.C.F. is 11, then the numbers are –
- A.
144 and 169
- B.
121 and 169
- C.
132 and 143
- D.
121 and 144
- E.
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Correct answer: C
To find the two numbers based on their ratio and Highest Common Factor (H.C.F.), follow these steps:
Step-by-Step Analysis
Understand the Relationship: When two numbers are in a given ratio, they can be expressed as multiples of that ratio's terms multiplied by their H.C.F.
Define the Variables:
The ratio of the two numbers is 12 : 13.
Let the common factor be x.
The two numbers can therefore be represented as 12x and 13x.
Apply the H.C.F.:
The H.C.F. is given as 11. In this context, the common factor x is equal to the H.C.F.
So, x = 11.
Calculate the Numbers:
First number = 12 * 11 = 132
Second number = 13 * 11 = 143