Question
Download Solution PDFThe difference between two numbers is 3630. The quotient and remainder are respectively 30 and 5 when the larger number is divided by the smaller one. Find the larger number.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The difference between two numbers = 3630.
Quotient when the larger number is divided by the smaller one = 30.
Remainder = 5.
Formula Used:
Larger Number = Smaller Number × Quotient + Remainder.
Difference between numbers = Larger Number - Smaller Number.
Calculation:
Let the smaller number be x .
Then, Larger Number = 30 × x + 5.
Also, Larger Number - Smaller Number = 3630.
Substitute Larger Number in the difference formula:
(30 × x + 5) - x = 3630
⇒ 30x + 5 - x = 3630
⇒ 29x + 5 = 3630
⇒ 29x = 3630 - 5
⇒ 29x = 3625
⇒ x = 3625 / 29
⇒ x = 125
Now, Larger Number = 30 × 125 + 5
⇒ Larger Number = 3750 + 5
⇒ Larger Number = 3755
The larger number is 3755.
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