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(#M40018606) ELITMUS Numerical Ability question Keep an EYE

The square of two digit no. is divided by half the no. After 36 added to the quotient,this sum is then divided by 2.the digits ao the resulting number are same as the original one but in the reverse order.How many numbers fulfill the same criteria?

(a)2 (b)4 (c)6 (d)7

Asked In Elitmus rohit goyal (11 years ago)

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Vinay Sipani   (11 years ago)

d) 7

Let no be (10x + y)

1st step => (10x+y)^2 / (1/2)*(10x+y) = 2*(10x+y) = 20x+2y
2nd step => (20x + 2y + 36)/2 = 10x + y + 18

=> 10x + y + 18 = 10y + x
=> 9(y-x) = 18
=> y - x = 2
=> (x,y) = (1,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)
=> 7 possibilities

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sonu sinha  (8 years ago)

2(10x+y)^2/(10x+y)=10y+x
10x+y+18=10y+x
9x-9y+18=0
9(x-y)=-18
x-y=-2
y-x=2
here (x,y)=(1,3),(3,5),(2,4),(4,6),(5,7),(6,8),(7,9)
so, there are 7 possibilities only..!

Is this solution Helpfull? Yes (4) | No   

GOVIND KUMAR GOYAL   (7 years ago)

first we take equation
((ab*ab)/(ab/2) +36)/2=ba
then we get
ab+18 =ba
1) 13+18=31
2) 24+18=42
3) 35 + 18=53
4) 46 + 18=64
5) 57 + 18=75
6) 68 + 18=86
7) 79 + 18=97

there are total 7 ways.

Is this solution Helpfull? Yes (1) | No   

ravi makawana  (9 years ago)

d) 7

Let no be (10x + y)

1st step => (10x+y)^2 / (1/2)*(10x+y) = 2*(10x+y) = 20x+2y
2nd step => (20x + 2y + 36)/2 = 10x + y + 18

=> 10x + y + 18 = 10y + x
=> 9(y-x) = 18
=> y - x = 2
=> (x,y) = (1,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)
=> 7 possibilities
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