Question
- Shri Jang Bahadur had Rs 6000 with him. He invested some money at 14% per annum and the balance at 15% per annum simple interest. After 2 years, he got Rs 1750 as interest. Find the sums invested by him at 14% and 15% respectively.
Answer: Option B
Let x be the amount invested at 14% and y be the amount invested at 15%.We know that x + y = 6000 (since that was the total amount he invested).We also know that the total interest earned after 2 years was Rs 1750.
Now, we can use the formula for simple interest to set up two equations:
Interest earned on the amount invested at 14%: I1 = x * 0.14 * 2 = 0.28xInterest earned on the amount invested at 15%: I2 = y * 0.15 * 2 = 0.3yTotal interest earned: I1 + I2 = 1750Substituting the first two equations into the third, we get:0.28x + 0.3y = 1750
We can then use the first equation (x + y = 6000) to solve for one of the variables in terms of the other:y = 6000 - x
Substituting this into the previous equation, we get:0.28x + 0.3(6000-x) = 17500.28x + 1800 - 0.3x = 1750-0.02x = -50x = 2500
So, he invested Rs 2500 at 14% and Rs 3500 at 15%.
Therefore, the answer is Option B (Rs 2500, Rs 3500).
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Let x be the amount invested at 14% and y be the amount invested at 15%.We know that x + y = 6000 (since that was the total amount he invested).We also know that the total interest earned after 2 years was Rs 1750.
Now, we can use the formula for simple interest to set up two equations:
Interest earned on the amount invested at 14%: I1 = x * 0.14 * 2 = 0.28xInterest earned on the amount invested at 15%: I2 = y * 0.15 * 2 = 0.3yTotal interest earned: I1 + I2 = 1750Substituting the first two equations into the third, we get:0.28x + 0.3y = 1750
We can then use the first equation (x + y = 6000) to solve for one of the variables in terms of the other:y = 6000 - x
Substituting this into the previous equation, we get:0.28x + 0.3(6000-x) = 17500.28x + 1800 - 0.3x = 1750-0.02x = -50x = 2500
So, he invested Rs 2500 at 14% and Rs 3500 at 15%.
Therefore, the answer is Option B (Rs 2500, Rs 3500).
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