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?​

Solve it


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Answer 1

Let :-

• No of mangoes (A) has = x
• No of mangoes (B) has = y

To Find :-

• No of mangoes (A) and (B) has = ?

Solution :-

• To calculate the no of mangoes for A and B at first we have to set up equation as per the given clue in the question. By solving equations we get the value for A and B.

Given in case - (i) :-

• A says to B, if you give 30 of your mangoes, I will have twice as many as left with you.

⇒ A + 30 = 2(B - 30)

⇒ x + 30 = 2(y - 30)

⇒ x + 30 = 2y - 60

⇒ x - 2y = -60 - 30

⇒ x - 2y = - 90---------(ii)

Given in case - (ii) :-

• B replies, if you give me 10, I will have thrice as many as left with you.

⇒ B + 10 = 3(A - 10)

⇒ y + 10 = 3(x - 10)

⇒ y + 10 = 3x - 30

⇒ 3x - y = 10 + 30

⇒ 3x - y = 40---------(ii)

• In equation (i) multiplying by 3 and equation (ii) multiplying by 1 then subtract.

⇒ 3x - 6y = - 270

⇒ 3x - y = 40

• By solving we get here :-

⇒ - 5y = - 310

⇒ 5y = 310

⇒ y = 62

• Putting the value of y = 62 in eq (i) :-

⇒ x - 2y = - 90

⇒ x - 2(62) = - 90

⇒ x - 124 = - 90

⇒ x = - 90 + 124

⇒ x = 34

Hence

• A has mangoes (x) = 34
• B has mangoes (y) = 62

Answer 2

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?

Answer :-

• A have 34 mangoes.
• B have 62 mangoes.

Explanation :-

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."

To Find :-

• How many mangoes does each have?

Solution :-

• Let A have m mangoes and B have n mangoes

✪ In 1st case :-

• A says to B, "if you give 30 of your mangoes, I will have twice as many as left with you."

Therefore,

↪ m + 30 = 2(n - 30)

↪ m + 30 = 2n - 60

↪ m = 2n - 60 - 30

➢ m = 2n - 90 – – – (1)

✪ In 2nd case :-

• B replies "if you give me 10, I will have thrice as many as left with you."

Therefore,

➵ n + 10 = 3(m - 10)

➵ n + 10 = 3m - 30

➵ 3m - n = 10 + 30

➪ 3m - n = 40 – – – (2)

From (1) put in (2) we get,

⇒ 3(2n - 90) - n = 40

⇒ 6n - 270 - n = 40

⇒ 6n - n = 40 + 270

⇒ 5n = 310

⇒ n = $\sf {\cancel{\dfrac{310}{5}}}$

➠ n = 62

Put value of 'n' in (1) we get,

↦ m = (2 × 62) - 90

↦ m = 124 - 90

➦ m = 34

Hence,

• A have mangoes = m = 34.
• B have mangoes = n = 62.

∴ A and B have 34 and 62 mangoes.

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