Let's analyze the problem step-by-step.
Problem Summary
- Total investment = Rs. 13,900
- Investment is divided into two schemes: A and B
- Both schemes have a simple interest rate of 1% per annum
- Total simple interest earned in 2 years = Rs. 8
- Find the amount invested in scheme B.
Step 1: Define variables
Let:
- Amount invested in scheme A = Rs. xxx
- Amount invested in scheme B = Rs. 13,900−x13,900-x13,900−x
Step 2: Write the simple interest formulas
Simple Interest (SI) = P×R×T100\frac{P\times R\times T}{100}100P×R×T Where:
- PPP = principal amount
- RRR = rate of interest per annum
- TTT = time in years
Given:
- R=1%R=1%R=1% for both schemes
- T=2T=2T=2 years
Step 3: Calculate total interest
Total interest from scheme A:
SIA=x×1×2100=2x100=0.02xSI_A=\frac{x\times 1\times 2}{100}=\frac{2x}{100}=0.02xSIA=100x×1×2=1002x=0.02x
Total interest from scheme B:
SIB=(13,900−x)×1×2100=0.02(13,900−x)SI_B=\frac{(13,900-x)\times 1\times 2}{100}=0.02(13,900-x)SIB=100(13,900−x)×1×2=0.02(13,900−x)
Total interest earned:
SIA+SIB=8SI_A+SI_B=8SIA+SIB=8
Substitute:
0.02x+0.02(13,900−x)=80.02x+0.02(13,900-x)=80.02x+0.02(13,900−x)=8
Step 4: Simplify the equation
0.02x+0.02×13,900−0.02x=80.02x+0.02\times 13,900-0.02x=80.02x+0.02×13,900−0.02x=8
0.02x−0.02x+278=80.02x-0.02x+278=80.02x−0.02x+278=8
278=8278=8278=8
This is not possible.
Observation
Since the interest rates are the same for both schemes (1% p.a.), and the time is the same, the total interest should be:
Total Interest=13,900×1×2100=27,800100=278\text{Total Interest}=\frac{13,900\times 1\times 2}{100}=\frac{27,800}{100}=278Total Interest=10013,900×1×2=10027,800=278
But the problem states the total interest is Rs. 8, which is inconsistent with the given rates and time.
Conclusion
There seems to be an inconsistency or typo in the problem statement:
- Both schemes have the same interest rate (1% p.a.)
- Total interest earned in 2 years on Rs. 13,900 at 1% p.a. should be Rs. 278, not Rs. 8.
Possible correction
If the interest rates are different for schemes A and B, or if the total interest is Rs. 80 (instead of 8), then the problem can be solved.
Please confirm or provide corrected interest rates or total interest
amount.
If you want, I can help solve the problem with corrected data!
