Question

Q6- A and B are partners in affirm sharing profit & loss in the Ratio of 2:1.They
decided to share future profile equally. Determine the scarifying & gaining ratio.​

Answer 1

Given :

• Old ratio of Partners A & B = 2 : 1

• New Ratio of Partners A & B = 1 : 1

To Find :

• Sacrificing Ratio

• Gaining Ratio

Solution :

${\boxed{\frak{\bullet \: sacrificing \: ratio \: = old \: ratio - new \: ratio}}}$

${\boxed{\frak{ \bullet \: gaining \: ratio = new \: ratio - old \: ratio}}}$

Sacrificing Ratio Of A :

$\: \to\sf \: \frac{2}{3} - \frac{1}{2} \\ \\ \to \sf \frac{2}{3} - \frac{1}{2} \: ( \: do \: cross \: multiply \: ) \\ \\ \to \sf \frac{4 - 3}{6} \\ \\ \to \bf \frac{1}{6}$

Sacrificing Ratio of B :

$\: \: \to\sf \: \frac{1}{3} - \frac{1}{2} \\ \\ \to \sf \frac{1 \times 2 - 3 \times 1}{3 \times 2} \\ \\ \to\sf \: \frac{2 - 3}{6} \\ \\ \to \bf \: \frac{ - 1}{6} = \frac{1}{6}$

Sacrificing Ratio Of Partners : 1 : 1

Gaining Ratio Of A :

$\: \: \: \to\sf \: \frac{1}{2} - \frac{2}{3} \\ \\ \to \sf \frac{1 \times 3 - 2 \times 2}{2 \times 3} \\ \\ \sf \to \: \frac{3 - 4}{6} \\ \\ \bf \to \: \frac{1}{6}$

Gaining Ratio Of B :

$\sf \to \: \frac{1}{2} - \frac{1}{3} \\ \\ \to \sf \: \frac{1 \times 3 - 2 \times 1}{2 \times 3} \\ \\ \sf \to \: \frac{3 -2 }{6} \\ \\ \sf \to \bf \frac{1}{6}$

Gaining Ratio Of Partners : 1 : 1

$\therefore \sf gaining \: ratio \: and \: sacrificing \: ratio \: of \: partners \: are \: same \: (1 : 1)$

Answer 2

A's sacrificing ratio is 1/6 and B's gaining ratio is 1/6

Given :

Old profit sharing ratio of A & B = 2 : 1

New profit sharing ratio of A & B = 1 : 1

To Find :

Sacrificing Ratio and Gaining Ratio

Solution :

Sacrificing ratio = old ratio - new ratio

Gaining ratio = new ratio - old ratio

Thus,

Sacrificing Ratio Of A =  $\frac{2}{3}$ - $\frac{1}{2}$

                                    =  $\frac{4-3}{6}$

                                    =  $\frac{1}{6}$

Sacrificing Ratio of B = $\frac{1}{3}$ - $\frac{1}{2}$

                                   =  $\frac{2-3}{6}$

                                   = -$\frac{1}{6}$

As we can see B's sacrificing ratio is a negative number because he is not sacrificing anything but actually gaining.

Gaining Ratio Of A = $\frac{1}{2}$ - $\frac{2}{3}$

                               = $\frac{3-4}{6}$

                               = $\frac{-1}{6}$

Here, A's gaining ratio is a negative number because he is not gaining anything but only sacrificing.

Gaining Ratio Of B = $\frac{1}{2}$ - $\frac{1}{3}$

                               = $\frac{3-2}{6}$

                               = $\frac{1}{6}$

Thus A's sacrificing ratio is 1/6 and B's gaining ratio is 1/6