# Moderate Algebra Solved QuestionAptitude Discussion

 Q. A number of three digits in base 7, when expressed in base 9, has its digits reversed in the order. What is the sum of the digits of the number?
 ✖ A. 5 ✖ B. 6 ✖ C. 7 ✔ D. 8

Solution:
Option(D) is correct

Only (0,1,2,3,4,5,6) can be the digits as base 7.

$(pqr)_7=(rqp)_9$

$\Rightarrow 7^2p+7^1q+7^0r =9^2r+9^1q+9^0p$

$\Rightarrow 49p+7q+r=81r+9q+p$

$\Rightarrow 48p=80r+2q$

$\Rightarrow 24p=40r+q$

After hit and trial,the number:

$pqr=(503)_7=(305)_9$

$\Rightarrow$  248 in the decimal system.

## (1) Comment(s)

Salman
()

any approach without hit and trial.