A two–digit number is 5 times the sum of its digits and is also equalto5 more than twice the product of its digits. Find the number.
Let the units digit be ‘Y’, so the tens digit will be X.
the number is 10X + Y
10X + Y = 5 (X + Y)
On simplifying further,
10X – 5X – 5Y + Y = 0
5X – 4Y = 0 –––––– (i)
10X + Y = 2XY + 5
10X– 2XY + Y – 5 = 0 –––––– (ii)
Putting the value of 
from equation –––––– (i)
40Y – 8Y2 + 5Y – 25 = 0
8Y2 – 45Y + 25 = 0
On applying Sreedhracharya formula
Y = 
or 5
∴ Y = 5
∴ 
from equation (i) 
∴ X = 4
∴ The number is 45 {4(10)+5}.
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