First slide

Arithmetic progression

Question

The digits of a three digit number $N$ are in A.P.If sum of the digits is 15 and the number obtained by re-versing the digits of the number is 594 less than the original number, then $\frac{1000}{N - 252}$ is equal to

Moderate

A

5/6
B

5/3
C

0.06
D

0.03

Solution

Let three digits of $N$ be: Hundred’s digit $= a - d$
ten’s digit $= a,$
and unit’s digit $= a + d$
$(a - d) + a + (a + d) = 15 f i a = 5$
and
$N = 100 (5 - d) + 50 + (5 + d)$ (1)
Number obtained by reversing digits of $N$ is
$N_{1} = 100 (5 + d) + 50 + (5 - d)$ (2)
Now,
$\begin{array}{l} 594 = N - N_{1} = 100 (- 2 d) + 2 d \\ \Rightarrow 2 d = - 6 \Rightarrow d = - 3 \end{array}$
Thus, $N$ = 852 and
$\frac{1000}{N - 252} = \frac{1000}{600} = \frac{5}{3}$

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