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Question

# In a two digit number, the ten's digit is bigger. The product of the digits is 27 and the difference between two digits is 6. Find the number.

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Solution

## Let the bigger number be 'a'. →the smaller number is 'a-6' Place value Face value Place value Face value 10 a 1 a-6 In expanded form the number becomes [10×a]+[1×(a−6)] → 10a + a - 6 = 11a - 6 ATQ:- →a x (a-6) = 27 →a2−6a=27 →a2−6a−27=0. →(a−9)(a+3)=0 →a=9ora=−3 CASE - I : When a = -3, the two digit number = 11a - 6 = -33 -6 = -39 This isn't the possible two digit number required as the bigger number should be at ten's place. CASE - II : When a = 9, the two digit number = 11a - 6 = 99 -6 = 93 Therefore, this is the possible two digit number required as the bigger number is at ten's place. Therefore, the 2-digit number is 93.

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