Question

Sum of two numbers is 103. If greater number is divided by smaller number then the quotient is 2 and the remainder is 19. Then find the numbers.

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Answer 1

SOLUTION

GIVEN

• Sum of two numbers is 103.

• If greater number is divided by smaller number then the quotient is 2 and the remainder is 19.

TO DETERMINE

The numbers

EVALUATION

Let the given numbers are x and y with x > y

Now it is given that Sum of two numbers is 103

x + y = 103 - - - - - (1)

Again when greater number is divided by smaller number then the quotient is 2 and the remainder is 19

So by the given condition

$\displaystyle \sf{ \frac{x - 19}{y} = 2}$

$\displaystyle \sf{ \implies \: x = 2y + 19 \: \: \: - - - - (2)}$

From Equation 1 and Equation 2 we get

2y + 19 + y = 103

$\sf{ \implies \: 3y + 19 = 103}$

$\sf{ \implies \: 3y = 84}$

$\sf{ \implies \: y = 28}$

From Equation 1 we get

x = 103 - 28 = 75

FINAL ANSWER

Hence the required numbers are 28 and 75

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