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A three-digit number is divided by 17 and leaves 5 as remainder. The sum of the digits of the divisible number is 7. If tenth digit of divisible number is 75% of its hundred’s digit and its hundred’s digit is 4 more than its unit digit, then what is the quotient?

A three-digit number is divided by 17 and leaves 5 as remainder. The sum of the digits of the divisible number is 7. If tenth digit of divisible number is 75% of its hundred’s digit and its hundred’s digit is 4 more than its unit digit, then what is the quotient? Correct Answer 25

Let the divisible number = 100x + 10y + z

Given,

x + y + z = 7      ---- (1)

Also given,

y = x × 75/100 = 3x/4      ---- (2)

And,

x – z = 4      ---- (3)

From equations (1), (2) and (3) :

x + (3x/4) + (x – 4) = 7

2x + 3x/4 = 11

x = 4, y = 3 and z = 0

The divisible number = 100 × 4 + 10 × 3 + 0 = 430

The quotient = (430 – 5)/17 = 25

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