A and B have certain number of mangoes. A says to B, " If you give me 10 of your mangoes, I will have twice as many as left with you." B replies, "If you give me 10 of your mangoes, I will have thrice the number of mangoes left with you. Find the original number of mangoes each had.

A had 22 mangoes, B had 26 mangoes

Step-by-step explanation:

We can write the following system:

A + 10 = 2(B - 10) -- Equation 1

3(A - 10) = B + 10 -- Equation 2

A + 10 = 2B - 20 → A = 2B - 30 -- Equation 3 (Simplify Equation 1)

3(2B - 30 - 10) = B + 10 -- Equation 4 (Substitute 3 into 2)

3(2B - 40) = B + 10

6B - 120 = B + 10

5B = 130

B = 26 -- (Solve for B in Equation 4)

A = 2 * 26 - 30 = 22 -- (Substitute B = 26 into Equation 3)

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