S.I = $\displaystyle \frac{15000 \times 15 \times 3}{100}$ = Rs.6750.
Amount = Principal + interest = Rs.15000 + Rs.6750 = Rs.21750.
S.I = $\displaystyle \frac{{24000 \times 12 \times 1\frac{1}{2}}}{100} = \frac{{24000 \times 12 \times \frac{3}{2}}}{100}$ = Rs.4320.
Amount = Principal + interest = Rs.24000 + Rs.4320 = Rs.28320.
Let the amount be 100.
Amount after 4 years = 100 x 1.5 = 150.
Interest = Total amount â€“ Principal = 150 â€“ 100 = 50.
Rate = $\displaystyle \frac{50}{4}$ = 12.5%.
Find the LCM of 15 and 12 => 60.
The rate of interest at 15% becomes 60% in => $\displaystyle \frac{60}{15}$ = 4 years.
The rate of interest at 12% becomes 60% in => $\displaystyle \frac{60}{12}$ = 5 years.
The sum in:
Â  5 years 
Â  =  Â  Rs.43750 

Â  Â  Â  Â  
Â  2 years 
Â  =  Â  Rs.32500 

Â  Â  Â  Â  
Diff 
Â  3 years 
Â  =  Â  Rs.11250 
Â  Â  Â  Â  Â 
For each year = $\displaystyle \frac{11250}{3}$ = 3750.
Total interest = 3750 x 5 = 18750.
Principal = 43750 â€“ 18750 = Rs.25000.
Principal = $\displaystyle \frac{\text{Simple Interest}}{\text{Rate} \times \text{Time}} \times 100$
Principal = $\displaystyle \frac{10800}{12 \times 3} \times 100$ = Rs.30000.
Rate = $\displaystyle \frac{\text{Simple Interest}}{\text{Principal} \times \text{Time}} \times 100$
Rate of interest = $\displaystyle \frac{8100}{18000 \times 3} \times 100$ = 15 or 15%.
Time = $\displaystyle \frac{\text{Simple Interest}}{\text{Principal} \times \text{Rate}} \times 100$
Time = $\displaystyle \frac{18000}{25000 \times 18} \times 100 = \frac{100}{25}$ = 4 years.
Simple interest = $\displaystyle \frac{14600 \times 10 \times \frac{125}{365}}{100}$ = 500.
Principal = P, Rate = 12%, Time = 2 years 9 months = $\displaystyle \frac{2.9}{12} = \frac{11}{4}$ years or $\displaystyle \frac{33}{36}$ months.
Interest paid by X = $\displaystyle \frac{{\text{P} \times 12 \times \frac{11}{4}}}{100} = \frac{33P}{100}$
Time for Y = 3 years 4 months = $\displaystyle \frac{3.1}{3}$ years = $\displaystyle \frac{10}{3}$ years or $\displaystyle \frac{40}{48}$ months.
Interest paid by Y = $\displaystyle \frac{{\text{P} \times 12 \times \frac{10}{3}}}{100} = \frac{4\text{P}}{100}$
=> $\displaystyle \frac{4\text{P}}{100}  \frac{33\text{P}}{100} = 1050 => \frac{40\text{P} â€“ 33\text{P}}{100}$ = 1050.
=> 7P = 105000 => P = $\displaystyle \frac{105000}{7}$ = 15000.
Descriptions  Status 

Attempted Questions  
UnAttempted Questions  
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Total Wrong Answers 
Principal: The money borrowed or lent out.
Interest: extra money paid or received on principal.
Simple interest is a rate of percent that calculated on principal only.
Simple Interest = $\displaystyle \frac{\text{P} \times \text{T} \times \text{R}}{100}$
P = Principal; T = Time; R = Rate of Interest.
Principal = $\displaystyle \frac{\text{Simple Interest}}{\text{Rate} \times \text{Time}} \times 100$
Rate = $\displaystyle \frac{\text{Simple Interest}}{\text{Principal} \times \text{Time}} \times 100$
Time = $\displaystyle \frac{\text{Simple Interest}}{\text{Principal} \times \text{Rate}} \times 100$
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