Question 108
Two numbers are in the ratio 4 : 7. If their HCF is 26. then the sum of these two numbers will be:
Solution
Let numbers be 4x & 7x
we know that,
$$LCM\times\ HCF=\ \Pr oduct\ of\ two\ numbers$$
$$LCM\times\ 26=\ 7x\times\ 4x$$
LCM=$$\frac{14}{13}x^2$$
now LCM of 7x & 4x =$$28x$$
$$\longrightarrow\ 28x=\frac{14}{13}x^2$$
$$x=26$$
the sum of two numbers = $$7x+4x=7\times\ 26+4\times\ 26=286\ Ans$$
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