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प्रश्न
If 460 is divided by a natural number, then quotient is 2 more than nine times the divisor and remainder is 5. Find the quotient and divisor.
उत्तर
Suppose divisor = x
∴ Quotient= 9x + 2
Dividend = 460 and remainder = 5
Dividend = Divisor × Quotient + Remainder
∴ 460 = x × (9x + 2) + 5
∴ 460 = 9x2 + 2x + 5
∴ 9x2 + 2x + 5 – 460 = 0
∴ 9x2 + 2x – 455 = 0
∴ 9x2 – 63x + 65x – 455 = 0
∴ 9x(x – 7) + 65(x – 7) = 0
∴ (9x + 65)(x – 7) = 0
∴ 9x + 65 = 0 or x – 7 = 0
∴ x = `(-65)/9` or x = 7
However, 460 is divided by a natural number, which cannot be negative.
∴ x = 7
∴Divisor = 7
∴ Quotient = 9 × 7 + 2 = 63 + 2 = 65
∴ Quotient is 65 and divisor is 7.
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