The middle digit of number between 100 and 1000 is zero and the sum of

1.	The middle digit of number between 100 and 1000 is zero and the sum of the other digits is 11. If the digits are reversed, the number so formed exceeds the original number by 495, then the number is ……………….. A) 405 B) 408 C) 308 D) 309
Answer» Correct option is (C) 308 Let the required number be a0b where 100's digit is a & 10's digit is zero (0) and unit digit is b. \(\therefore\) a0b = 100a + 10 \(\times\) 0 + b \(\Rightarrow\) a0b = 100a + b __________(1) Sum of other digits is a+b. a+b = 11 __________(2) (Given) If digits are reversed then formed number be b0a. \(\therefore\) b0a = 100b + a __________(3) According to given condition, we have 100b+a = 100a + b + 495 \(\Rightarrow\) 99b - 99a = 495 \(\Rightarrow\) b - a = \(\frac{495}{99}\) = 5 \(\Rightarrow\) b - a = 5 __________(4) Adding equation (2) & (4), we get (a+b) + (b - a) = 11+5 \(\Rightarrow\) 2b = 16 \(\Rightarrow\) b = \(\frac{16}2\) = 8 \(\therefore\) a = 11 - b = 11 - 8 = 3 (From (2)) Hence, the required number is 100a+b = 300+8 = 308. (From (1)) Correct option is C) 308

The middle digit of number between 100 and 1000 is zero and the sum of the other digits is 11. If the digits are reversed, the number so formed exceeds the original number by 495, then the number is ……………….. A) 405 B) 408 C) 308 D) 309

Answer»

Correct option is (C) 308

Let the required number be a0b where 100's digit is a & 10's digit is zero (0) and unit digit is b.

\(\therefore\) a0b = 100a + 10 \(\times\) 0 + b

\(\Rightarrow\) a0b = 100a + b __________(1)

Sum of other digits is a+b.

a+b = 11 __________(2) (Given)

If digits are reversed then formed number be b0a.

\(\therefore\) b0a = 100b + a __________(3)

According to given condition, we have

100b+a = 100a + b + 495

\(\Rightarrow\) 99b - 99a = 495

\(\Rightarrow\) b - a = \(\frac{495}{99}\) = 5

\(\Rightarrow\) b - a = 5 __________(4)

Adding equation (2) & (4), we get

(a+b) + (b - a) = 11+5

\(\Rightarrow\) 2b = 16

\(\Rightarrow\) b = \(\frac{16}2\) = 8

\(\therefore\) a = 11 - b

= 11 - 8 = 3 (From (2))

Hence, the required number is 100a+b = 300+8 = 308. (From (1))

Correct option is C) 308