Question

Gaurav and Saurabh are sharing profits and losses equally. They agree to share profits in the ratio of 3:2 _______ is a

gaining partner:--[Gaurav/ Saurabh/ both/ none of these]​

Answer 1

Answer:

Gaurav is Gaining partner.

Explanation:

Solution :

Gaurav and Saurabh are sharing profits and losses equally

Old Ratio :

Gaurav : Saurabh = 1 : 1

• Gaurav's Share = $\dfrac{1}{2}$

• Saurabh's Share = $\dfrac{1}{2}$

They agree to share profits in the ratio of 3:2

New Sharing Ratio =

• Gaurav : Saurabh = 3 : 2

• Gaurav's New Share = $\dfrac{3}{5}$

• Saurabh's New Share = $\dfrac{2}{5}$

★ Gaining Ratio :

Gaining Ratio = New Ratio - Old Ratio

• Gaurav =

$\sf{\longrightarrow{\dfrac{3}{5} \: - \: \dfrac{1}{2} \: = \: \dfrac{(6 \: - \: 5)}{10}}}$

$\sf{\longrightarrow{\dfrac{1}{10} \: - - - - \: (Gain)}}$

• Saurabh =

$\sf{\longrightarrow{\dfrac{2}{5} \: - \: \dfrac{1}{2} \: = \: \dfrac{(4 \: - \: 5)}{10}}}$

$\sf{\longrightarrow{\dfrac{( - \: 1)}{10} \: - - - - \: (Sacrifice)}}$

• Gaurav's Gain = $\dfrac{1}{10}$

Therefore, Gaurav is Gaining partner.

Answer 2

Answer:

Given :-

• Gaurav and Saurabh are sharing profits and losses equally.
• They agree to share profits in the ratio of 3 : 2.

To Find :-

• Who is the gaining partner.

Formula Used :-

$\clubsuit$ Gaining Ratio Formula :

$\mapsto\: \sf\boxed{\bold{\pink{Gaining\: Ratio =\: New\: Ratio\: -\: Old\: Ratio}}}$

Solution :-

${\small{\bold{\purple{\underline{\leadsto\: In\: case\: of\: Old\: Ratio\: :-}}}}}$

Given :

$\leadsto$ Gaurav and Saurabh = 1 : 1

❒ Gaurav Old Ratio :

$\implies \sf Old\: Ratio_{(Gaurav)} =\: \dfrac{1}{1 + 1}$

$\implies \sf \bold{\green{Old\: Ratio_{(Gaurav)} =\: \dfrac{1}{2}}}$

❒ Saurabh Old Ratio :

$\implies \sf Old\: Ratio_{(Saurabh)} =\: \dfrac{1}{1 + 1}$

$\implies \sf \bold{\green{Old\: Ratio_{(Saurabh)} =\: \dfrac{1}{2}}}$

${\small{\bold{\purple{\underline{\leadsto\: In\: case\: of\: New\: Ratio\: :-}}}}}$

➲ Gaurav and Saurabh agree to share profits in the ratio of 3 : 2.

❒ Gaurav New Ratio :

$\implies \sf New\: Ratio_{(Gaurav)} =\: \dfrac{3}{3 + 2}$

$\implies \sf\bold{\green{New\: Ratio_{(Gaurav)} =\: \dfrac{3}{5}}}$

❒ Saurabh New Ratio :

$\implies \sf New\: Ratio_{(Saurabh)} =\: \dfrac{2}{3 + 2}$

$\implies \sf\bold{\green{New\: Ratio_{(Saurabh)} =\: \dfrac{2}{5}}}$

Now, we have to find the gaining ratio of Gaurav and Saurabh :

$\bigstar\: \tt{Gaining\: Ratio\: Of\: Gaurav\: :-}$

Given :

$\leadsto\: \rm{\bold{New\: Ratio =\: \dfrac{3}{5}}}$

$\leadsto\: \rm{\bold{Old\: Ratio =\: \dfrac{1}{2}}}$

According to the question by using the formula we get,

$\longrightarrow \sf Gaining\: Ratio_{(Gaurav)} =\: \dfrac{3}{5} - \dfrac{1}{2}$

$\longrightarrow \sf Gaining\: Ratio_{(Gaurav)} =\: \dfrac{6 - 5}{10}$

$\longrightarrow \sf\bold{\red{Gaining\: Ratio_{(Gaurav)} =\: \dfrac{1}{10}\: \: \bigg\lgroup \sf\bold{Gain}\bigg\rgroup}}$

$\bigstar\: \tt{Gaining\: Ratio\: of\: Saurabh\: :-}$

Given :

$\leadsto \rm{\bold{New\: Ratio =\: \dfrac{2}{5}}}$

$\leadsto \rm{\bold{Old\: Ratio =\: \dfrac{1}{2}}}$

According to the question by using the formula we get,

$\longrightarrow \sf Gaining\: Ratio_{(Saurabh)} =\: \dfrac{2}{5} - \dfrac{1}{2}$

$\longrightarrow \sf Gaining\: Ratio_{(Saurabh)} =\: \dfrac{4 - 5}{10}$

$\longrightarrow \sf\bold{\red{Gaining\: Ratio_{(Saurabh)} =\: \dfrac{- 1}{10}\: \: \bigg\lgroup \sf\bold{Sacrifices}\bigg\rgroup}}$

$\therefore$ The gaining partner is Gaurav.

Hence, the correct options is option no (1) Gaurav.