Multiple choice

Kamla can complete a piece of work in 24 days. Nirmala can complete the same work in 18 days. Kamla starts the work alone and works for X days. After that, Nirmala alone finishes the remaining work in Y days, completing the work in a total of 20 days. If X and Y are both positive integers, select the correct option.

  1. 4 X Y + 1 is an even integer.

  2. 2X + Y = 22

  3. X - Y is an odd integer.

  4. X2 + 1 is a multiple of 13.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Kamla's rate = 1/24, Nirmala's rate = 1/18. Kamla works X days, Nirmala works Y days. X + Y = 20. Work done = X/24 + Y/18 = 1. Multiply by 72: 3X + 4Y = 72. Substitute Y = 20 - X: 3X + 4(20 - X) = 72, so 3X + 80 - 4X = 72, X = 8. Then Y = 12. Check options: X^2 + 1 = 64 + 1 = 65, which is 5 * 13.

AI explanation

Using the LCM method, the total work is 72 units, where Kamla's rate is 3 units per day and Nirmala's rate is 4 units per day. This sets up the equation 3X + 4Y = 72, with the condition that X plus Y equals 20. Solving this system of equations yields X equals 8 and Y equals 12. When X is 8, X squared plus 1 equals 65, which is exactly 5 times 13, making the statement that X squared plus 1 is a multiple of 13 the correct result.

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