Question

32 times of a two digit number is 23 times the number obtained by reversing its digit. The sum of its digit is 15 Find the number:

a. 96

b. 69

c. 87

d. Insufficient information

Answer 1

Dear Student,

Answer: 69 ( option B)

Solution:

Let the two digit number is xy

so, sum of digits is given as x+y = 15

32 times of the  digit number is 23 times the number obtained by reversing its digit.

32 (xy) = 23(yx)

now this information of equation 2 is represented as

32( 10x+y) = 23( 10y +x)

320x +32y= 230y+23x

320 x - 23x = 230y-32y

297x = 198 y  

y = (297/198)x

y = 1.5 x ------- put this in eq x+y = 15

x+1.5 x = 15

2.5x =15

x = 15/2.5

x = 6

now again put the value of x in equation x+y = 15

6+ y = 15

y = 15-6

y = 9

So,the number  is 69.

Verification:  32 ×69 = 2208

32 × 96 = 2208

Hope it helps you.

Answer 2

Acc to the question, let the two digit number be (10x+y).

Now, 32 times of (10x+y) will be 32 * (10x+y) = (320x+32y).

23 times the number obtained by reversing its digit = 23 * (10y+x) = (230y+23x).

Acc to the question,  (320x+32y) = (230y+23x)

or, 297x = 198y

or, 27x = 18y.

or, 3x = 2y.

or, x = 2y/3.

Now the smartest way will be to test the options.

First option 96 doesn't satisfy this equation, whereas the second option i.e. 69 satisfies it.

Therefore, the two digit number is 69.