Question

Arun and Ajoy started a business jointly by investing ₹ 24000 and ₹ 30000 respectively at the begining of the year. But after a few months Arun invested ₹ 12000 more. After a year the profit was ₹ 14030 and Arun received the profit share of ₹ 7130. Let us find after how many months did does Arun invest money in that business.​

Answer 1

Answer:

Given :-

$\leadsto$ Arun and Ajoy started a business jointly by investing Rs 24000 and Rs 3000 respectively at the begining of the year.

$\leadsto$ After a few months Arun invested Rs 12000 more .

$\leadsto$ After a year the profit was Rs 14030 and Arun received the profit share of Rs 7130 .

To Find :-

$\leadsto$ How many months did does Arun invest money in that business .

Solution :-

Let, Arun contribute Rs 12000 more after x month .

Arun contributed Rs 24000 for x month and Rs (24000 +12000 ) = Rs 36000 for (12 -x ) month.

If total profit will have to get for 1 month Arun will require,

=> Rs { 24000 × x + 36000 × (12 -x ) }

=> Rs (432000 - 12000x )

Ajoy contribute Rs 30000 for 12 month .

If Total profit will have to get in 1 month

Ajoy will require Rs (30000 × 12 ) = Rs 360000

$\mapsto$ Ratio of principal of Arun and Ajoy,

=> ( 432000 - 12000x ) : 360000

=> (432 - 12x ) : 360

=> (36 - x ) : 30

Profit is divided in the ratio of their principal

Total profit of Arun 14030 × $\dfrac{36 - x}{66 - x}$

According to the question,

=> 14030 × $\dfrac{36 - x}{66 - x}$ = 7130

=> $\dfrac{36 - x}{66 - x}$ = $\dfrac{7130}{14030}$

=> $\dfrac{36 - x}{66 - x}$ = $\dfrac{713}{1403}$

[ By doing cross multiplication we get ]

=> 50508 - 1403x = 47058 -713x

=> 1403x - 713x = 50508 - 47058

=> 690x = 3450

=> x = 5

$\therefore$ Arun joined the business after 5 months .

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Answer 2

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