Question 61

The HCF and LCM of two numbers are 8 and 224 respectively. If the ratio of the two numbers is 4:7, then the greater of the two numbers is:

Solution

If the ratio of the two numbers is 4:7.

Let's assume the numbers are 4y and 7y respectively.

The HCF and LCM of two numbers are 8 and 224 respectively.

$$HCF\times\ LCM\ =\ first\ number\ \times\ \sec ond\ number$$

$$8\times224\ =\ 4y\times 7y$$

$$8\times224\ =\ 28y^2$$

$$8\times8\ =\ y^2$$

$$8^2\ =\ y^2$$

y = 8
Greater number = 7y

= $$7\times8$$

= 56

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