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Q.

A two digit number is 4 times the sum of its digits and twice the product of the digits. Find the number.


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a

53

b

42

c

63

d

36 

answer is D.

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Detailed Solution

Given that a two-digit number is 4 times the sum of its digits and twice the product of the digits.
Let x be the digit in the ones place and y be the digit in the tens place.
So, the two-digit number = 10y + x.
Since, given that number = 4 times sum of its digits, we get
⇒10y+x=4 x+y ⇒10y+x=4x+4y ⇒10y−4y=4x−x ⇒6y=3x ⇒y= 3x 6 ⇒y= x 2 ⇒x=2y …………..(1)
Also, given number = 2 times product of its digits,
⇒10y+x=2xy …………(2)
Divide equation (2) by xy on both the sides.
⇒ 10y xy + x xy = 2xy xy ⇒ 10 x + 1 y =2 ………….(3)
Put x = 2y from equation (1) in equation (3).
⇒ 10 2y + 1 y =2 ⇒ 10 2y + 1 y × 2 2 =2 ⇒ 10 2y + 2 2y =2 ⇒ 10+2 2y =2 ⇒ 12 2y =2
⇒ 6 y =2 ⇒ 6 2 =y ⇒y=3
Put y= 3 in equation (1).
⇒x=2 3 ⇒x=6
Put x= 6 and y= 3 in equation 10y + x.
Two-digit number is,
=10×3+6 =30+6 =36 So, the two-digit number is 36.
The correct option is (4).
 
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A two digit number is 4 times the sum of its digits and twice the product of the digits. Find the number.