The LCM of the two quotients obtained when two numbers a and b are divided by their HCF is 77. LCM of another pair of quotients. when other two numbers c and d have the same HCF as that of a and b, and when divided by it is 221. Which of the following could be the ratio of the sum of a and b to that of the difference between c and d?

4 : 17

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11 : 4

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2 : 9

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39 : 2

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Solution

The correct option is D 39 : 2
Let HCF (a, b) = k
Then $a = 77 \times H C F (a, b) = 77 k$
b = HCF (a, b) = k
(a + b) = 78k ...(i)
$a = 17 \times H C F (a, b) o r 13 \times H C F (a, b)$
= 17k or 13k
$d = 13 \times H C F (a, b) o r 17 \times H C F (a, b)$
= 13k or 17k
$\frac{a + b}{| c - d |} = \frac{78 k}{4 k} = \frac{39}{2}$

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The correct option is D 39 : 2Let HCF (a, b) = k Then a=77×HCF (a,b)=77k b = HCF (a, b) = k (a + b) = 78k ...(i) a=17×HCF (a,b) or 13×HCF (a,b) = 17k or 13k d=13×HCF (a,b) or 17×HCF (a,b) = 13k or 17k a+b|c−d|=78k4k=392