ICSE Class X Math 2014 Solved Paper

Question : 44 of 52

Marks: +1, -0

A two digit positive number is such that the product of its digits is 6 . If 9 is added to the number, the digits interchange their places. Find the number.

Solution:

Let the required two digit number be

10 x+

y

Given :

x y=6

and

10 x+y+9=10 y+x

\;10 x-x+y-10 y+9\;=0

⇒\;9 x-9 y+9\;=0

⇒\;x-y+1\;=0

⇒\;y\;=x+1

\;x y\;=6 \;\text " (given) "\;

⇒\;x(x+1)\;=6

⇒ x^2+x-6\;=0

⇒\;x^2+3 x-2 x-6\;=0

⇒\;(x+3)(x-2)\;=0

⇒\;x\;=-3,2

\;\;\text " Rejecting "\;\;x\;=-3

\;\text " When "\; x=2, y=x+1=2+1=3

∴

The required two digit number

\;=10 x+y

\;=10 × 2+3=23

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