Answer:

Step-by-step explanation:

Let's denote the original amount as

�

P and the profit rate as

�

R.

The profit after 3 years is given as

�

+

3

�

�

=

1578

P+3RP=1578, and after 5 years it is

�

+

5

�

�

=

1830

P+5RP=1830.

Now, we can set up a system of two equations to solve for

�

P and

�

R:

�

+

3

�

�

=

1578

P+3RP=1578

�

+

5

�

�

=

1830

P+5RP=1830

Let's solve these equations:

From equation (1):

�

+

3

�

�

=

1578

P+3RP=1578

From equation (2):

�

+

5

�

�

=

1830

P+5RP=1830

Subtracting equation (1) from equation (2):

(

�

+

5

�

�

)

−

(

�

+

3

�

�

)

=

1830

−

1578

(P+5RP)−(P+3RP)=1830−1578

Simplify:

2

�

�

=

252

2RP=252

Divide by 2:

�

�

=

126

RP=126

Now substitute this value into equation (1) to find

�

P:

�

+

3

×

126

=

1578

P+3×126=1578

�

+

378

=

1578

P+378=1578

�

=

1200

P=1200

So, the original amount (

�

P) is Rs 1200, and the profit rate (

�

R) is 126.

Verified answer

Answer:

Formula used:

Profit % = Profit/CP × 100

Profit = SP – CP

Here, SP and CP are selling price and cost price respectively

Calculation:

Let the selling price be 100x

Profit = 25% of 100x = 25x

Now, Profit = SP – CP

⇒ 25x = 100x – CP

⇒ CP = 75x

Now, Profit % = Profit/CP × 100

⇒ 25x/75x × 100 = 100/3% = 33.33%

∴ The actual profit is 33.33%

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