AIOU Solved Assignment Code 1349 Introduction To Business Mathematics Autumn 2023 Assignment 1.pdf

ALLAMA IQBAL OPEN UNIVERSITY ISLAMABAD
(Department of Mathematics)
Course: Introduction to Business Mathematics (1349)
Semester: Autumn, 2023
Level: HSSC
ASSIGNMENT No. 1
Q.1 (a) Divide Rs.80000 in the ratio 2:6
To divide Rs. 80,000 in the ratio of 2:6, follow these steps:
Step 1: Find the total parts in the ratio.
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The total parts in the ratio 2:6 is 2 + 6 = 8.
Step 2: Determine the value of one part.
To find the value of one part, divide the total amount by the total number of
parts:
Value of one part = Rs. 80,000 / 8 = Rs. 10,000
So, each part is worth Rs. 10,000.
Step 3: Allocate the amount according to the ratio.
Now, you can distribute the total amount based on the ratio.
For the 2 parts, allocate 2 parts X Rs. 10,000 per part = Rs. 20,000.
For the 6 parts, allocate 6 parts X Rs. 10,000 per part = Rs. 60,000.
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So, you divide Rs. 80,000 into Rs. 20,000 and Rs. 60,000 according to the
ratio 2:6.
(b) Express 58.5% to a common fraction.
To express 58.5% as a common fraction, follow these steps:
Step 1: Convert the percentage to a decimal.
58.5% can be expressed as a decimal by dividing it by 100:
58.5% = 58.5 / 100 = 0.585
Step 2: Express the decimal as a common fraction.
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To do this, you need to convert the decimal into a fraction. Since 0.585 has
three decimal places, we'll multiply both the numerator and denominator by
1000 to remove the decimal:
0.585 = 0.585/1 = (0.585 X 1000)/(1 X 1000) = 585/1000
Step 3: Simplify the fraction.
To simplify the fraction, find the greatest common divisor (GCD) of the
numerator and denominator, and then divide both by the GCD:
GCD of 585 and 1000 = 5
Divide both the numerator and denominator by 5:
(585 ÷ 5) / (1000 ÷ 5) = 117/200
So, 58.5% is equivalent to the common fraction 117/200.
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Q.2 (a) Price of one dozen oranges is Rs.50. Find the selling price, if they
all are sold at the profit of 14%.
To find the selling price of one dozen (12) oranges when they are sold at a
profit of 14%, you can follow these steps:
Step 1: Find the cost price of one orange.
Cost Price (CP) of one dozen oranges = Rs. 50
To find the cost price of one orange, divide the cost of one dozen by 12 (since
there are 12 oranges in a dozen):
Cost Price of one orange = Rs. 50 / 12 = Rs. 4.1667 (rounded to four decimal
places)
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Step 2: Calculate the profit on one orange.
Profit Percentage = 14%
Profit on one orange = (Profit Percentage / 100) X Cost Price of one orange
Profit on one orange = (14 / 100) X Rs. 4.1667
Profit on one orange ≈ Rs. 0.5833 (rounded to four decimal places)
Step 3: Find the selling price of one orange.
Selling Price (SP) of one orange = Cost Price (CP) of one orange + Profit on
one orange
Selling Price of one orange = Rs. 4.1667 + Rs. 0.5833
Selling Price of one orange ≈ Rs. 4.75 (rounded to two decimal places)
Step 4: Find the selling price of one dozen oranges.
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Since there are 12 oranges in a dozen, multiply the selling price of one orange
by 12 to find the selling price of one dozen oranges:
Selling Price of one dozen oranges = Rs. 4.75 (per orange) X 12 = Rs. 57
So, the selling price of one dozen oranges, when sold at a 14% profit, is Rs.
57.
(b) A ring was sold for Rs.980 on 2% loss. Find the cost price of the ring.
To find the cost price of the ring, given that it was sold for Rs. 980 at a 2%
loss, you can follow these steps:
Step 1: Identify the loss percentage.
Loss Percentage = 2%
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Step 2: Calculate the loss amount.
Loss Amount = (Loss Percentage / 100) X Selling Price
Loss Amount = (2 / 100) X Rs. 980
Loss Amount = (2/100) X Rs. 980 = Rs. 19.60
Step 3: Find the cost price.
Cost Price (CP) = Selling Price (SP) + Loss Amount
CP = Rs. 980 + Rs. 19.60
CP = Rs. 999.60
So, the cost price of the ring is Rs. 999.60.
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Q.3 (a) Price of a toy is Rs.250, discount offers on this toy @ 20%. Find
the amount of discount and discounted price.
To find the amount of discount and the discounted price of the toy when there
is a 20% discount on its original price of Rs. 250, follow these steps:
Step 1: Calculate the discount amount.
Discount Percentage = 20%
Discount Amount = (Discount Percentage / 100) X Original Price
Discount Amount = (20 / 100) X Rs. 250
Discount Amount = (1/5) X Rs. 250
Discount Amount = Rs. 50
So, the amount of the discount is Rs. 50.
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Step 2: Calculate the discounted price.
Discounted Price = Original Price - Discount Amount
Discounted Price = Rs. 250 - Rs. 50
Discounted Price = Rs. 200
The discounted price of the toy is Rs. 200, and the amount of the discount is
Rs. 50.
(b) Ali is a distributor of a calculator company he booked an order of 25
calculators @ Rs.650 per calculator and agreed to allow 12% trade
discount. Calculate the value of the invoice.
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To calculate the value of the invoice for Ali's order of 25 calculators with a
price of Rs. 650 per calculator and a 12% trade discount, follow these steps:
Step 1: Calculate the total cost before the trade discount.
Total Cost before Discount = Number of Calculators × Price per Calculator
Total Cost before Discount = 25 calculators × Rs. 650 per calculator
Total Cost before Discount = Rs. 16,250
Step 2: Calculate the trade discount.
Trade Discount Percentage = 12%
Trade Discount Amount = (Trade Discount Percentage / 100) X Total Cost
before Discount
Trade Discount Amount = (12 / 100) X Rs. 16,250
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Trade Discount Amount = (3/25) X Rs. 16,250
Trade Discount Amount = Rs. 1,950
Step 3: Calculate the value of the invoice.
Value of the Invoice = Total Cost before Discount - Trade Discount Amount
Value of the Invoice = Rs. 16,250 - Rs. 1,950
Value of the Invoice = Rs. 14,300
So, the value of the invoice for Ali's order of 25 calculators with a 12% trade
discount is Rs. 14,300.
Q.4 (a) Find the interest on Rs.2180 for one year at simple interest 4%.
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To find the interest on Rs. 2,180 for one year at a simple interest rate of 4%,
follow these steps:
Step 1: Convert the percentage to a decimal.
Interest Rate = 4%
Interest Rate as a decimal = 4% / 100 = 0.04
Step 2: Use the simple interest formula:
Simple Interest (SI) = (Principal Amount × Rate × Time) / 100
Where:
Principal Amount (P) = Rs. 2,180
Rate (R) = 0.04 (as calculated in Step 1)
Time (T) = 1 year
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Now, plug these values into the formula:
SI = (2,180 × 0.04 × 1) / 100
SI = (87.2) / 100
SI = Rs. 0.872
So, the interest on Rs. 2,180 for one year at a simple interest rate of 4% is Rs.
0.872.
(b) Ahmed borrowed Rs.2 lac at 5% simple interest and invested the same
amount at 5% compounded quarterly. Calculate what he gains after 6
years?
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To calculate what Ahmed gains after 6 years when he borrows Rs. 2,00,000 at
5% simple interest and invests the same amount at 5% compounded quarterly,
you'll need to find the interest he pays on the loan and the final amount he
accumulates from the investment.
Let's start with the simple interest:
Step 1: Calculate the simple interest on the loan.
Principal Amount (P) = Rs. 2,00,000
Rate of Interest (R) = 5%
Time (T) = 6 years
Simple Interest (SI) = (P X R X T) / 100
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SI = (2,00,000 X 5 X 6) / 100
SI = (10,00,000) / 100
SI = Rs. 10,000
Ahmed pays Rs. 10,000 in simple interest on the loan over 6 years.
Now, let's calculate the compound interest he earns from the investment:
Step 2: Calculate the compound interest.
Principal Amount (P) = Rs. 2,00,000
Rate of Interest (R) = 5% per annum (or 1.25% per quarter)
Number of Compounding Periods per Year (n) = 4 (compounded quarterly)
Time (T) = 6 years
Using the compound interest formula:
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A = P X (1 + (R/n))^(nXT)
A = 2,00,000 X (1 + (0.05/4))^(4 X 6)
A = 2,00,000 X (1 + 0.0125)^(24)
A = 2,00,000 X (1.0125)^24
A ≈ 2,00,000 X 1.34392
A ≈ Rs. 2,68,784.01
The total amount Ahmed accumulates from the investment after 6 years is
approximately Rs. 2,68,784.01.
Now, to calculate the gain, subtract the interest paid on the loan from the
amount accumulated from the investment:
Gain = Amount Accumulated - Interest Paid
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Gain ≈ Rs. 2,68,784.01 - Rs. 10,000
Gain ≈ Rs. 2,58,784.01
So, Ahmed gains approximately Rs. 2,58,784.01 after 6 years.
Q.5 (a) Calculate the difference between compound interest and simple
interest both are charge on Rs.3500 at the rate 25% annually for 6 years.
To calculate the difference between compound interest and simple interest
when both are charged on Rs. 3,500 at an annual interest rate of 25% for 6
years, follow these steps:
Step 1: Calculate the simple interest.
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Simple Interest (SI) is calculated using the formula:
SI = (P X R X T) / 100
Where:
P = Principal amount (Rs. 3,500)
R = Rate of interest per annum (25% or 0.25 as a decimal)
T = Time in years (6 years)
SI = (3,500 X 0.25 X 6) / 100
SI = (875 X 6) / 100
SI = 525 / 100
SI = Rs. 5.25
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Step 2: Calculate the compound interest.
Compound Interest (CI) is calculated using the formula:
Where:
P = Principal amount (Rs. 3,500)
R = Annual interest rate (25% or 0.25 as a decimal)
n = Number of times interest is compounded per year (assuming it's
compounded annually, so n = 1)
T = Time in years (6 years)
First, we calculate the amount (A) that will be in the account after 6 years:
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Now, we can calculate the compound interest:
CI = A - P
CI = Rs. 14,619.87 - Rs. 3,500
CI ≈ Rs. 11,119.87
Step 3: Find the difference between compound interest and simple interest.
Difference = Compound Interest - Simple Interest
Difference ≈ Rs. 11,119.87 - Rs. 5.25
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Difference ≈ Rs. 11,114.62
So, the difference between the compound interest and simple interest when
both are charged on Rs. 3,500 at an annual interest rate of 25% for 6 years is
approximately Rs. 11,114.62.
(b) 35% commission is offered to an agent by a manufacturer to sale his
old stock. The commission that agent received is of Rs.28,000. Calculate
the amount received by the manufacturer.
To calculate the amount received by the manufacturer when a 35%
commission is offered to an agent and the agent receives Rs. 28,000 as
commission, follow these steps:
Step 1: Calculate the total sale amount.
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The agent's commission is 35% of the total sale amount, which is Rs. 28,000.
So, let "X" be the total sale amount:
35% of X = Rs. 28,000
To solve for X, you can divide both sides of the equation by 0.35 (which is
35% as a decimal):
X = Rs. 28,000 / 0.35
X = Rs. 80,000
So, the total sale amount is Rs. 80,000.
Step 2: Calculate the amount received by the manufacturer.
The manufacturer receives the total sale amount minus the agent's
commission. In this case, the manufacturer receives:
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Amount received by the manufacturer = Total sale amount - Agent's
commission
Amount received by the manufacturer = Rs. 80,000 - Rs. 28,000
Amount received by the manufacturer = Rs. 52,000
The amount received by the manufacturer is Rs. 52,000.
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AIOU Solved Assignment Code 1349 Introduction To Business Mathematics Autumn 2023 Assignment 1.pdf

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