Product of a positive number of two digits and the digit in its unit's place is #189#. If the digit in the ten's place is twice of that in the unit's place, what is the digit in the unit's place ?

Question

617 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-22T06:10:51

# 3#.

Note that the two digit nos. fulfilling the second condition (cond.)

are, #21,42,63,84.#

Among these, since #63xx3=189#, we conclude that the two digit

no. is #63# and the desired digit in unit's place is #3#.

To solve the Problem methodically, suppose that the digit of

ten's place be #x,# and that of unit's, #y#.

This means that the two digit no. is #10x+y#.

#"The "1^(st)" cond. "rArr (10x+y)y=189#.

#"The "2^(nd)" cond. "rArr x=2y#.

Sub.ing #x=2y# in #(10x+y)y=189, {10(2y)+y}=189#.

#:. 21y^2=189 rArr y^2=189/21=9 rArr y=+-3#.

Clearly, #y=-3# is inadmissible.

#:. y=3,# is the desired digit, as before!

Enjoy Maths.!