Question

2. Virat 'and Samrat together invested 50000 and 120000 rupees to start a business. They suffered a loss of 20%. How much loss did each of them incur?
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Answer 1

Answer:

Loss incurred by Virat = Rs.10000

Loss incurred by Samrat = Rs.24000

Step-by-step explanation:

Money invested by Virat =Rs.50,000

Money invested by Samrat =Rs.1,20,000

Then,

Loss incurred by Virat =Rs.(50000× 20/100 )= Rs.10000

Loss incurred by Samrat =Rs.(120000× 20/100 )= Rs.24000

Answer 2

Given :

• Money invested by Virat = Rs. 50,000 & Money invested by Samrat = Rs. 12,0000.
• Loss = 20%

To Find :

• Loss incurred by each of them.

Calculations :

Firstly let's calculate the total amount of money invested by both Virat & Samrat.

• Money invested by Virat = Rs. 50,000

• Money invested by Samrat = Rs. 12,0000

And their ratios are :-

$\mapsto \sf 50,000 : 12,0000$

$\mapsto\sf \dfrac{50,000}{12,0000}$

• By cancelling zeroes,

$\mapsto\sf \dfrac{50}{12}$

$\mapsto \bf 5 : 2$

• So, their ratios are 5 : 2.

Now let's add up both the amounts,

$\rightarrow \rm Rs. \: 5000 + Rs. \: 12,0000$

• On adding the numbers,

$\rightarrow \bf Rs. \: 170,000$

Therefore, total amount invested by Virat & Samrat is Rs. 170,000.

Now, let's calculate the total loss by both of them [Virat & Samrat],

Formula :

• $\boxed{ \rm{ \green{Loss = \left[ \dfrac{Loss \%}{100} \times Total \: investment \right] }}}$

$\longrightarrow\sf Loss = \left[ \dfrac{20}{100} \times Rs. 170,000 \right] \\ \\ \longrightarrow\sf Loss = \left[ \dfrac{20}{100} \times Rs. \: 170,000 \right] \\ \\ \longrightarrow\sf Loss = 0.2 \times Rs. \: 170,000 \\ \\ \longrightarrow\rm{ \pmb{ \pink{\boxed{Loss = Rs. \: 34000}}}} \: \blue{ \bigstar}$

• Hence, total loss by Virat & Samrat is Rs. 34000.

$\dag$ According to the Question,

Let's calculate the loss incurred by each of them [Virat & Samrat].

As we know that, we took ratios of 50000 : 120000 as 5 : 12

So,

• Ratio of Virat = 5
• Ratio of Samrat = 12

So, sum of both ratios is 17 [5 + 12 = 17]

Let's divide the total loss of investment and the sum of both the ratios,

$\rightarrow \bf x = \cancel \dfrac{34000}{17} \\ \\ \rightarrow{\boxed{\bf x = 2000}}$

Now, in the end let's multiply both the ratios [5 and 12] with Rs. 2000.

$\star{ \rm{\pmb {\underline{ \red{Loss \: incured \: by \: Virat \: -}}}}}$

$\longrightarrow \rm 5 \times 2000 \\ \\ \longrightarrow \bf 10,000$

$\star{ \rm{\pmb {\underline{ \red{Loss \: incured \: by \: Samrat \: -}}}}}$

$\longrightarrow \rm 12 \times 2000 \\ \\ \longrightarrow \bf 24,000$

Therefore,

• Loss incurred by Virat = Rs. 10,000
• Loss incurred by Samrat = Rs. 24,000

$\dag$ Verification :

We know that, total loss incurred by both of them is Rs. 34000. So, let's check whether our answer is correct or not.

⇒ Rs. 10,000 + Rs. 24, 000 = Rs. 34,000

⇒ Rs. 34,000 = Rs. 34,000

⇒ L.H.S = R.H.S

Hence, verified!

$\pink{\star}$ Point to remember :

• L.H.S means left hand side.
• R.H.S means right hand side.