A and B each have a certain number of mangoes. A says to B, "if you give 30 of your mangoes, I will have twice as many as left with you." B replies, "if you give me 10, I will have thrice as many as left with you." How many mangoes does each have?
Answers
If A and B each have a certain number of mangoes and A says to B, "if you give 30 of your mangoes, I will have twice as many as left with you," for which B replies, "if you give me 10, I will have thrice as many as left with you." Then the number of mangoes each have are:
A has 10 mangoes and B has 20 mangoes.
1. Let the number of mangoes A have be 'a' and the number of mangoes B have be 'b'.
2. According to the first constraint the first equation can be formulated as a+30=2b.
3. According to the second constraint the second equation can be formulated as b+10=3a.
4. Multiplying the second equation by 2 and substituting this new equation in the first equation gives us
a+30=6a-20
=> 5a=50
=>a=10
Substituting the value of a in first equation gives us
(10)+30=2b
=>2b=40
=>b=20
Thus, A has 10 mangoes and B has 20 mangoes.