# Numbers

(PQRSTU) × 6 = STUPQR, where P, Q, R, S, T, U are single and distinct digits and PQRSTU is a six digit number, find the number PQRSTU.

### See our previous ‘Questions of the Day’:

1. Nikita Chawla

As the no. of digits have to be 6 after multiplying , so the only possibility for P was 1. Since , this no. is getting multiplied by 6 , so , S>6. R could be 2/4/6/8. Now, 6*S+3= P(1). So the only value satisfying the conditions was S=8. U had to be an odd no. Then all the values of R could be eliminated except for 2 ( since every digit had to be distinct). After that , got all the values , and the no, 857142(no. after multiplying by 6) was also satisfying the divisibility by 6.

2. rishabh_831

Sir
Can you explain the solution as im unable to trace the origin of 3 in calculation of s.

1. rishabh_831

Ive used another approach
1qr*6000 + stu*6 = stu*1000 +1qr

youl will get ratio of
1qr/stu =142/857

• Nice instruction, thanks

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