Question

A person earms 15% on an investment but loses 10% on another investment. If the ratio of the two investments be 3: 5. What is the gain or loss on the two investments taken together?



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Answer 1

Let :-

• The first one investment = 3x
• The another investment = 5x

To Find :-

• Gain or loss on two investment = ?

Solution :-

To calculate loss or gain on two investment taken together at first we have to set up equation by helping clue in the question.

Calculation for 1st investment :-

[Principal = 3x. Gain = 15%]

⇒ Amount for 1st investment = (100 + G%)/100 × P

⇒ Amount = 115/100 × 3x

⇒ Amount = 69x/20

Calculation for 2nd investment :-

[Principal = 5x. Loss = 10%]

⇒ Amount for 2nd investment = (100 - L%)/100 × P

⇒ Amount = 90/100 × 5x

⇒ Amount = 90x/20

Now calculate total amount and principal :-

⇒ Total principal = Total investment

⇒ Total principal = 3x + 5x = 8x

⇒ Total amount = Amount 1st + Amount 2nd

⇒ Total amount = 69x/20 + 90x/20

⇒ Total amount = (69x + 90x)/20

⇒ Total amount = 159x/20

Here find which is greater principal or amount :-]

⇒Amount = 159x/20 Principal = 8x/1

• Comparing between them we get :-]

⇒ Amount = 159x × 1 = 159x

⇒ Principal = 8x × 20 = 160x

• Here Amount < Principal so, we have loss

⇒ Loss = Principal - Amount

⇒ Loss = 8x/1 - 159x/20

⇒ Loss = (160x - 159x)/20

⇒ Loss = x/20

⇒L% = L × 100/P

⇒L% = x/20 × 100/8x

⇒L% = 5x/8x => 5/8 = 0.625%

Hence, the person has loss = 0.625% :-]

Answer 2

STEP-BY-STEP EXPLANATION:

.

Let the first investment and second investment are 3x

and 5x respectively.

The sum he gets from 1st investment = 15% of 3x + 3x

• ➺ The Amount from 1st investment = 15/100 × 3x + 3x
• ➺ The Amount from 1st investment = 45x/100 + 3x
• ➺ The Amount from 1st investment = 9x/20 + 3x
• ➺ The Amount from 1st investment = (9x + 60x)/20

The sum he gets from 1st investment is 69x/20.

The sum he gets from 2nd investment = 5x - 10% of 5x

• ➺ The sum he gets from 2nd investment = 5x - 10/100 × 5x
• ➺ The sum he gets from 2nd investment = 5x - x/2
• ➺ The sum he gets from 2nd investment = (10x - x)/2

The sum he gets from 2nd investment is 9x/2.

The total sum he gets from both investments = 69x/20 + 9x/2

• ➺ The total sum he gets from both investments = (69x + 90x)/20

The total sum he gets from both investments is 159x/20.

The total sum he invested is 8x.

Here,

• 8x > 151x/20

So,

• There is loss.

Loss = CP - SP

• ➺ Loss = 8x - 159x/20
• ➺ Loss = (160x - 159x) / 20

Loss is x/20.

Loss Percentage = L/CP × 100

• ➺ Loss Percentage = (x/20)/8x × 100
• ➺ Loss Percentage = x/20 × 1/8x × 100
• ➺ Loss Percentage = 5/8%

REQUIRED ANSWER,

• There is loss of 5/8 or 0.625%.