Explanation for the Arithmetic Quiz 03

This is the detailed explanation for the Arithmetic Quiz 03. Each question’s solution is broken down step-by-step to help you understand the core concepts and formulas.

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1. What is the simple interest on a sum of Rs. 700 if the rate of interest for the first 3 years is 8% per annum and for the last 2 years is 7.5% per annum?

Answer: Rs. 269.5

• Step 1: Calculate the interest for the first 3 years. SI1​=(Principal×Rate1​×Time1​)/100 SI1​=(700×8×3)/100=16800/100=Rs. 168
• Step 2: Calculate the interest for the last 2 years. SI2​=(Principal×Rate2​×Time2​)/100 SI2​=(700×7.5×2)/100=10500/100=Rs. 105
• Step 3: Calculate the total simple interest. Total SI = SI1​+SI2​=168+105=Rs. 273

Note: The calculated answer is Rs. 273, which is an option. The provided correct answer of Rs. 269.5 seems to be a mistake in the original source material. We will proceed with the correct calculation.

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2. Find the simple interest on Rs. 5200 for 2 years at 6% per annum.

Answer: Rs. 624

• Step 1: Use the simple interest formula. $SI=(Principal\times Rate\times Time)/100$
• Step 2: Plug in the values. $SI=(5200\times 6\times 2)/100=62400/100=\text{Rs. }624$

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3. Rs. 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years.

Answer: Rs. 1380

• Step 1: Calculate the simple interest. $SI=(1200\times 5\times 3)/100=18000/100=\text{Rs. }180$
• Step 2: Calculate the total amount. Amount = Principal + Simple Interest Amount = $1200+180=\text{Rs. }1380$

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4. What is the difference between the simple interest on a principal of Rs. 500 being calculated at 5% per annum for 3 years and 4% per annum for 4 years?

Answer: Rs. 5

• Step 1: Calculate the simple interest for the first scenario. SI1​=(500×5×3)/100=7500/100=Rs. 75
• Step 2: Calculate the simple interest for the second scenario. SI2​=(500×4×4)/100=8000/100=Rs. 80
• Step 3: Find the difference. Difference = SI2​−SI1​=80−75=Rs. 5

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5. Find the principal if the interest compounded at the rate of 10% per annum for two years is Rs. 420.

Answer: Rs. 2000

• Step 1: Use the compound interest formula. CI=P[(1+R/100)T−1]
• Step 2: Plug in the known values and solve for the principal (P). 420=P[(1+10/100)2−1] 420=P[(1.10)2−1] $420=P[1.21-1]$ $420=P[0.21]$ $P=420/0.21=\text{Rs. }2000$

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6. Find the difference between the simple interest and the compound interest at 5% per annum for 2 years on principal of Rs. 2000.

 

Answer: 5

• Step 1: Calculate the simple interest (SI). $SI=(2000\times 5\times 2)/100=20000/100=\text{Rs. }200$
• Step 2: Calculate the compound interest (CI). CI=P[(1+R/100)T−1] CI=2000[(1+5/100)2−1] CI=2000[(1.05)2−1] $CI=2000[1.1025-1]=2000[0.1025]=\text{Rs. }205$
• Step 3: Find the difference. Difference = $CI-SI=205-200=\text{Rs. }5$

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7. Find the rate of interest if the amount after 2 years of simple interest on a capital of Rs. 1200 is Rs. 1440.

Answer: 10%

• Step 1: Calculate the simple interest earned. $SI=\text{Amount}-\text{Principal}=1440-1200=\text{Rs. }240$
• Step 2: Use the simple interest formula to find the rate (R). $SI=(P\times R\times T)/100$ $240=(1200\times R\times 2)/100$ $240=24R$ $R=240/24=10\%$

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8. Find the compound interest on Rs. 1000 at the rate of 20% per annum for 18 month when interest is compounded half yearly.

Answer: Rs. 331

• Step 1: Adjust the rate and time for half-yearly compounding. The interest is compounded half-yearly, so the number of compounding periods for 18 months is $18/6=3$. The rate per period is half of the annual rate: $20\%/2=10\%$.
• Step 2: Calculate the compound amount (A). A=P(1+R/100)T A=1000(1+10/100)3=1000(1.10)3=1000×1.331=Rs. 1331
• Step 3: Calculate the compound interest. $CI=A-P=1331-1000=\text{Rs. }331$

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9. Interest obtained on a sum of Rs. 5000 for 3 years is Rs. 1500. Find the rate percent.

Answer: 10%

• Step 1: Use the simple interest formula to find the rate (R). $SI=(P\times R\times T)/100$
• Step 2: Plug in the known values. $1500=(5000\times R\times 3)/100$ $1500=50\times 3\times R$ $1500=150R$ $R=1500/150=10\%$

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10. Rs. 2100 is lent at compound interest of 5% per annum for 2 years. Find the amount after two years.

Answer: Rs. 2315.25

• Step 1: Use the compound amount formula. A=P(1+R/100)T
• Step 2: Plug in the values. A=2100(1+5/100)2=2100(1.05)2 $A=2100(1.1025)=\text{Rs. }2315.25$