CMAT 2015 Solved Question Paper

Question : 9 of 100

Marks: +1, -0

When a two digit number is multiplied by the sum of its digits, 405 is obtained. On multiplying the number written in reverse order of the same digits i.e. by the sum of digits, 486 is obtained. Find the number.

Validate

Solution:

(b) Let the digits at unit’s and ten's places be x and y, respectively
Then, number = 10 y + x
∴ (10 y + x)(y + x) = 405
and (10x + y)(y + x) = 486
The number should be factors of 405,
405 =5x3x3x3x3

\;\;\;\;\;\;\;

= 5 x

3^4

(15 x 27) and (45 x 9) are the two options only,
45 x 9 = (10 x 4 + 5) (4 + 5)
Only satisfies the above two conditions.
Hence, the required answer is 45.

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