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Count or maximise positive integer solutions of ax + by = c (buying two items)

This type of question, asked 3 times: CDS 1 2017, CDS 1 2019, CDS 1 2020. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2017

    40
    Sunil wants to spend Rs. 200 on two types of sweets, costing Rs. 7 and Rs. 10 respectively. What is the maximum number of sweets he can get so that no money is left over ?

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  2. Question 2

    CDS 1 2019

    74
    A person carries Rs. 500 and wants to buy apples and oranges out of it. If the cost of one apple is Rs. 5 and the cost of one orange is Rs. 7, then what is the number of ways in which a person can buy both apples and oranges using total amount ?

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  3. Question 3

    CDS 1 2020

    42
    How many integral values of xx and yy satisfy the equation 5x+9y=75x + 9y = 7, where −500<x<500-500 < x < 500 and −500<y<500-500 < y < 500?

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