1. Problem 1: Complete the tables by finding missing values in each. **Table 1: Discounts and Sale Prices** Given: Selling Price (SP), Rate of Discount (r), Discount (D), Sale Price (S). The relation is: $$ D = SP \times r $$ $$ S = SP - D $$ (1) For SP=500, r=20% = 0.20: $$ D = 500 \times 0.20 = 100 $$ $$ S = 500 - 100 = 400 $$ (2) For SP=950, r=35% = 0.35: $$ D = 950 \times 0.35 = 332.50 $$ $$ S = 950 - 332.50 = 617.50 $$ (3) Given r=25% = 0.25 and D=250: $$ SP = \frac{D}{r} = \frac{250}{0.25} = 1000 $$ $$ S = SP - D = 1000 - 250 = 750 $$ (4) Given r=12% = 0.12 and D=574.20: $$ SP = \frac{574.20}{0.12} = 4785 $$ $$ S = SP - D = 4785 - 574.20 = 4210.80 $$ (5) Given SP=9455 and D=3782: $$ r = \frac{D}{SP} = \frac{3782}{9455} \approx 0.4 = 40\% $$ $$ S = SP - D = 9455 - 3782 = 5673 $$ **Table 2: Mark-up and Selling Prices** Relation: $$ Mark\text{-}up\ Price = Original\ Price \times Mark\text{-}up\ Rate $$ $$ Selling\ Price = Original\ Price + Mark\text{-}up\ Price $$ (1) Given OP=300, r=10% =0.10: $$ Mark\text{-}up\ Price = 300 \times 0.10 = 30 $$ $$ Selling\ Price = 300 + 30 = 330 $$ (2) OP=1055, r=12% = 0.12: $$ Mark\text{-}up\ Price = 1055 \times 0.12 = 126.60 $$ $$ Selling\ Price = 1055 + 126.60 = 1181.60 $$ (3) Given r=25% = 0.25, Mark-up Price=275: $$ Original\ Price = \frac{275}{0.25} = 1100 $$ $$ Selling\ Price = 1100 + 275 = 1375 $$ (4) Given r=18% = 0.18, Mark-up Price=1713.60: $$ Original\ Price = \frac{1713.60}{0.18} = 9520 $$ $$ Selling\ Price = 9520 + 1713.60 = 11233.60 $$ (5) Given OP=11563, Mark-up Price=1734.45: $$ Mark\text{-}up\ Rate = \frac{1734.45}{11563} \approx 0.15 = 15\% $$ $$ Selling\ Price = 11563 + 1734.45 = 13297.45 $$ **Table 3: Commission** Relation: $$ Commission = Total\ Sales \times Rate $$ (1) TS=5000, r=5% = 0.05: $$ Commission = 5000 \times 0.05 = 250 $$ (2) TS=12560, r=8% = 0.08: $$ Commission = 12560 \times 0.08 = 1004.80 $$ (3) Given r=14% = 0.14, Commission=2864.12: $$ Total\ Sales = \frac{2864.12}{0.14} = 20458 $$ (4) Given r=15% = 0.15, Commission=8350.50: $$ Total\ Sales = \frac{8350.50}{0.15} = 55670 $$ (5) Given TS=112545, Commission=28136.25: $$ Rate = \frac{28136.25}{112545} = 0.25 = 25\% $$ **Table 4: Simple Interest (SI)** Formula: $$ SI = P \times r \times t $$ where $P$=Principal, $r$=rate per year in decimal, $t$=time in years. Note: Convert months to years where needed. (1) P=8000, r=1% = 0.01, t=1year: $$ SI=8000 \times 0.01 \times 1 = 80 $$ (2) P=12000, r=2% = 0.02, t=2 years: $$ SI=12000 \times 0.02 \times 2 = 480 $$ (3) P=15500, r=5% = 0.05, t=18 months = 1.5 years: $$ SI=15500 \times 0.05 \times 1.5 = 1162.50 $$ (4) P=21680, r=0.5% = 0.005, t=5 years: $$ SI=21680 \times 0.005 \times 5 = 542 $$ (5) P=24742, r=1.25% = 0.0125, t=9 months = 0.75 years: $$ SI=24742 \times 0.0125 \times 0.75 = 232.72 $$ (6) Given P=4200, t=4 years, SI=252: $$ r = \frac{SI}{P \times t} = \frac{252}{4200 \times 4} = 0.015 = 1.5\% $$ (7) Given t=6 months=0.5 years, SI=73.70: Assuming $P$ and $r$ unknown, insufficient data to compute missing values. (8) P=6700, r=4% = 0.04, t=0.25 year: $$ SI=6700 \times 0.04 \times 0.25 = 67 $$ The value 120 given suggests a misalignment; possibly $P$ or $t$ differs. (9) Given r=12% = 0.12, t=3.5 years, SI=15000: $$ P = \frac{SI}{r \times t} = \frac{15000}{0.12 \times 3.5} = 35714.29 $$ (10) Given r=10% = 0.10, SI=3742.50: Assuming missing $P$ and $t$, insufficient data to solve. (11) P=49900, no other data to calculate missing info. **Summary of filled tables:** Table 1: Discounts and Sale Prices: | Selling Price | Rate of Discount | Discount | Sale Price | |---------------|------------------|----------|------------| | 500 | 20% | 100 | 400 | | 950 | 35% | 332.50 | 617.50 | | 1000 | 25% | 250 | 750 | | 4785 | 12% | 574.20 | 4210.80 | | 9455 | 40% | 3782 | 5673 | Table 2: Mark-up and Selling Prices: | Original Price | Mark-up Rate | Mark-up Price | Selling Price | |----------------|--------------|--------------|---------------| | 300 | 10% | 30 | 330 | | 1055 | 12% | 126.60 | 1181.60 | | 1100 | 25% | 275 | 1375 | | 9520 | 18% | 1713.60 | 11233.60 | | 11563 | 15% | 1734.45 | 13297.45 | Table 3: Commissions: | Total Sales | Rate | Commission | |-------------|-------|------------| | 5000 | 5% | 250 | | 12560 | 8% | 1004.80 | | 20458 | 14% | 2864.12 | | 55670 | 15% | 8350.50 | | 112545 | 25% | 28136.25 | Table 4: Simple Interests: | Principal Amount | Rate | Time | Simple Interest | |------------------|-------|-----------|-----------------| | 8000 | 1% | 1 year | 80 | | 12000 | 2% | 2 years | 480 | | 15500 | 5% | 1.5 years | 1162.50 | | 21680 | 0.5% | 5 years | 542 | | 24742 | 1.25% | 0.75 year | 232.72 | | 4200 | 1.5% | 4 years | 252 | | (data missing) | | 0.5 year | 73.70 (not solved) | | 6700 | 4% | 0.25 year | 67 (approx) | | 35714.29 | 12% | 3.5 years | 15000 | | (data missing) | 10% | (unknown) | 3742.50 (no solution) | | 49900 | (unknown) | (unknown) | (unknown) |