The product of two 2-digit numbers is 535 and their GCD is 7. Find their LCM.
Answers 2
Answer:
57
Step-by-step explanation:
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>>A two digit number is such that the prod
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A two digit number is such that the product of the digits is 35, when 18 is added to the number, the digits interchange their places. Find the number.
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Correct option is A)
Solution:-
Let the two digit no. be xy.
Then its decimal expansion becomes 10×x+y
When digits are interchanged, the number is yx.
Then its decimal expansion becomes 10×y+x
x×y=35{Given}
⇒x=
y
35
⟶(i)
Given that when 18 is added to the number, the digits are interchanged
∴(10x+y)+18=(10y+x)
⇒9x−9y+18=0
⇒9(x−y+2)=0
⇒x−y+2=0
⇒
y
35
−y+2=0{from (i)}
⇒35−y
2
+2y=0
⇒y
2
−2y−35=0
⇒(y+5)(y−7)=0
∵y
=−5
∴y=7
Substituting the value of y in (i), we get
x=
7
35
=5
Hence the two digit no. is 57.
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Author:
earllyons
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The Nos are 25 and 21
Explanation is in the pic
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dobie
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