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Answer :
The greater number in a pair of numbers with an LCM of 84, an HCF of 21, and a ratio of 1:4 is found to be 84 (option a). This is calculated by establishing the relationship between the numbers, their LCM, and HCF.
The question asks to find the greater number when given the Least Common Multiple (LCM), the Highest Common Factor (HCF), and the ratio of two numbers. The LCM is given as 84, and the HCF is 21. The ratio of the two numbers is 1:4.
Step-by-Step Solution:
- Let's denote the smaller number as x and the greater number as 4x, according to the ratio 1:4.
- We know that the product of two numbers is equal to the product of their LCM and HCF, so x imes 4x = 84 imes 21.
- Simplifying gives us x extsuperscript{2} = (84 imes 21) / 4 = 441.
- Taking the square root of both sides, we get x = 21.
- The greater number therefore is 4x = 4 imes 21 = 84.
The correct answer is (a) 84, as it is the greater number in the pair.
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