Question

new ratio of B:C - 3:1, old ratio of A:B:C- 2:3:1,Gain ratio of B:C-???​

Answer 1

ANSWER :

• ❖ If new ratio of B : C is 3 : 1 and old ratio of A : B : C is 2 : 3 : 1; then Gain ratio of B : C is 3 : 1.

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SOLUTION :

❒ Given :-

• New ratio of B : C is 3 : 1.

• Old ratio of A : B : C is 2 : 3 : 1.

❒ To Calculate :-

• Gain ratio of B : C = ?

❒ Required Formula :-

• $\dag \: \: \underline{ \boxed{ \bold{ \: Gain = New \: \: Share - Old \: \: Share \: }}}$

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❒ Calculation :-

It is given that,

• New ratio of B : C is 3 : 1.

Thus,

• New Share of B = $\sf{\dfrac{3}{4}}$

• New Share of C = $\sf{\dfrac{1}{4}}$

Again,

• Old ratio of A : B : C is 2 : 3 : 1.

Thus,

• Old Share of B = $\sf{\dfrac{3}{6}}$

• Old Share of C = $\sf{\dfrac{1}{6}}$

Now,

Using the formula of Gain, we get,

• ★ Gain of B = New Share of B - Old Share of B

⇒ Gain of B = $\sf{\dfrac{3}{4}}$ - $\sf{\dfrac{3}{6}}$

⇒ Gain of B = $\sf{\dfrac{9 - 6}{12}}$

⇒ Gain of B = $\sf{\dfrac{3}{12}}$

And,

• ★ Gain of C = New Share of C - Old Share of C

⇒ Gain of C = $\sf{\dfrac{1}{4}}$ - $\sf{\dfrac{1}{6}}$

⇒ Gain of C = $\sf{\dfrac{3 - 2}{12}}$

⇒ Gain of C = $\sf{\dfrac{1}{12}}$

Therefore,

• ✪ Gain Ratio of B : C = Gain of B : Gain of C

➨ Gain Ratio of B : C = $\sf{\dfrac{3}{12}}$ : $\sf{\dfrac{1}{12}}$

∴ Gain Ratio of B : C = 3 : 1