Question

In a three digit number, unit's digit is 2/ 3 times of ten's digit and 3/ 4 times of hundred's digit. If the number formed by reversing the digits subtracted from the original number, is equal to 198, then the sum of original number and number formed by reversing the digits can be​

Answer 1

Answer:

Sum of original number and reversed number = 1594

Step-by-step explanation:

Let the number be 100x + 10y + z

We are given that,

z = (2/3) y ------- 1

and

z = (3/4) x ------ 2

The New number formed when reversed is 100z + 10y + x

According to the Question,

(100x + 10y + z) - (100z + 10y + x) = 198

198 = 100x + 10y + z - 100z - 10y - x

198 = 99x - 99z

198 = 99(x - z)

198/99 = x - z

x - z = 2 ----- 3

From eq.2 and eq.3 we get,

x - (3/4)x = 2

(4/4)x - (3/4)x = 2

(1/4)x = 2

x = 8

then,

z = (3/4)x

z = (3/4)(8)

z = 3 × 2

z = 6

Also,

From eq.1 we get,

z = (2/3)y

6 = (2/3)y

6 × 3 = 2y

18/2 = y

y = 9

Hence, the original number is 896 and its reversed number is 698

Sum = 896 + 698

Sum = 1594

Hope it helped and you understood it........All the best.