Question

A number consists of three digits, the right-hand digit being zero. If the left hand and the middle digits be interchanged the number is diminished by 180. If the left-hand digit be halved and the middle and right-hand digits be interchanged the number is diminished by 454. Find the number. [Hint. Let the original number be 100a+10b+ 0, i.e., 100a+10b, then, by the first condition (100a+10b)-(100b + 10a) = 180 ⇒a-b=2 a By the second condition, new number = 100 x = +0+ b = 50a + b 2 and so (100a+10b) - (50a + b) = 454 ⇒ 50a + 9b = 454]. .​

Answer 1

860

Explanation:

number = 100a + 10b +0

100b + 10a +180 = 100a + 10b

90a-90b=180

a-b=2

a = b+2

100(a/2) +10*0 + b + 454 = 100a + 10b

50a + b +454 = 100a +10b

50a+9b = 454

50(b+2) + 9b = 454

50b+100+9b = 454

59b = 354

b = 6

a = 6+2 = 8

100*8+10*6 = 860