On dividing a larger number by a smaller number, the quotient obtained is 6 and the remainder is 30. What is the smaller number if the difference between the two numbers is 1380?
a) 280
b) 290
c) 270
d) 250
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Given,
Quotient = 6
Remainder = 30
Difference between the two numbers = 1380
Let the smaller number (divisor) be X.
Therefore, the larger number (dividend) is X + 1380
By using the division formula,
Dividend = Divisor × Quotient + Remainder
X + 1380 = X × 6 + 30
X + 1380 = 6X + 30
1380 = 5X + 30
1350 = 5X
X = 1350/5
X = 270
Therefore, the smallest number is 270 and the largest number is 270 + 1380 = 1650.
Verification: 1650 ÷ 270 = 6 with a remainder of 30.