Question 55

The LCM of two numbers is 4 times their HCF. The sum of LCM and HCF is 125. If one of the numbers is 100, then the other number is

Solution

Let one of the numbers = $$x$$ and other number = 100

Let L.C.M = $$L$$ and H.C.F = $$H$$

According to ques, => $$L=4H$$ --------------(i)

and $$L+H=125$$

Substituting value from equation (i), we get : $$4H+H=5H=125$$

=> $$H=\frac{125}{5}=25$$

=> $$L=4\times25=100$$

Thus, product of numbers = $$L\times H$$

=> $$100\times x=100\times25$$

=> $$x=25$$

=> Ans - (B)

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