Question

The sum of the digits of a 2- digit no. Is 10. The no. is 16 times the units digit. Find the no.

Answer 1

Let  the digits of a 2-digit no. be x and y
The no. = 10x+y 
The sum of their digits = 10
⇒ x+y = 10 -----------(1)
The no. = 16× units digit 
⇒ 10x+y = 16y
⇒ 10x + y - 16y = 0
⇒ 10x - 15y = 0
⇒ 5(2x - 3y) = 0
⇒ 2x - 3y = 0  --------------(2)
solving (1) and (2) by substitution method
    in eq(1)
x+y =10
⇒ x = 10-y   ----------------(3)
substituting (3) in (2)
    2(10 - y) - 3y = 0
⇒ 20 - 2y - 3y = 0
⇒ 20 - 5y = 0
⇒ 20 = 5y
⇒ 5y = 20
⇒ y = 20/5
∴ y = 4
∴ x = 10-y
⇒ x = 10-4
∴ x= 6
∴ The no = 10x + y
= (10× 6) + 4
= 60 + 4
= 64