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?

Question

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?

Philoid · Accepted Answer

Let the number of mangoes A has be ‘a’ and number of mangoes B has be ‘b’.

Given, . 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”

⇒ a + 30 = 2(b – 30)

⇒ a = 2b – 90 --------- (1)

Also, b + 10 = 3(a – 10)

⇒ b = 3a – 40 ---------- (2)

Substituting value of a from eq1 in eq2

⇒ b = 6b – 270 – 40

⇒ 5b = 310

⇒ b = Rs. 62

Substituting value of b in eq1

⇒ a = 124 – 90

⇒ a = Rs. 34