Find the numbers if the HCF of two numbers is 47 and their sum is 188.
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Correct answer: B
Explanation
The correct answer is option 2 i.e. 47 and 141.
The two numbers be ( x) and ( y).
(HCF) (x, y) = 47
( x + y = 188 )
⇒ x = 47a , y = 47b
⇒ HCF (a, b) = 1
⇒ x + y = 188
⇒ 47a + 47b = 188
⇒ 47(a + b) = 188
⇒ a + b = 4
( a = 1) and ( b = 3)
( a = 3 ) and ( b = 1)
If ( a = 1) and ( b = 3 ),
⇒ x = 47 × 1 = 47 , y = 47 × 3 = 141
If ( a = 3 ) and ( b = 1 ),
⇒x = 47 × 3 = 141 , y = 47 × 1 = 47
Therefore the two numbers are 47 and 141.