Social Arithmetic: Overall Value, Theory and Formulas and Example Problems

Social Arithmetic: Overall Value, Theory and Formulas and Example Problems – Do you understand what is meant by social arithmetic? On this occasion About the knowledge.co.id will discuss about Social Arithmetic and the things that surround it. Let's look at the discussion in the article below to understand it better.

Social Arithmetic: Overall Value, Theory and Formulas and Example Problems

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Social arithmetic is the application of the basics of mathematical calculations in everyday social life such as trade, banking and others. To understand social arithmetic, you must understand algebraic material, operations for calculating fractions and percents so that it is easier to discuss this material.

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Overall Value and Per-Unit Value

The overall value is the total value of all existing units, while the per-unit value is the value per one unit of goods or products.

As an example:

It is known that the price of each laptop unit is IDR 4,000,000. A company will buy 12 laptops for work operations.

Then, calculate the overall value as well as the per-unit value?

Answer:

Value per unit = IDR 4,000,000
Overall value = 12 x IDR 4,000,000 = IDR 48,000,000

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Theory and Formulas

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  Profit and loss

Profit is selling price > buying price
Profit = selling price – buying price
Profit Percentage :

% Profit= (big profit) / (purchase price) × 100%

The loss is selling price < buying price
Loss = purchase price – selling price

Loss Percentage :

% Loss = (loss) / (purchasing price) × 100%

Example:
A rice trader buys 1 ton of rice for IDR 9,150,000. The rice will be resold at Rp 9,500 per kg. In order to sell the rice, the trader must provide plastic as a wrapper for Rp 67,000. Calculate how much profit and loss?
Answer:
Buying price of rice per kg = Buying price of rice + Plastic wrap
= IDR 9,150,000 + IDR 67,000
= IDR 9,217,000/ton
= IDR 9,217/kg
Selling price per kg = IDR 9,500/kg
The selling price is higher than the buying price, so the trader makes a profit.
Profit = IDR 9,500 – IDR 9,217
= IDR 283/kg = IDR 283,000/ton

Profit and Loss Percentage

To measure sales performance, traders usually calculate profit and loss percentages. Profit and Loss Percentage Formula:

Profit or loss percentage = profit or loss / purchase price x 100%

Example:
Using the example above, calculate the percentage of profit earned by the rice trader?
Answer:
Profit percentage = IDR 283/ IDR 9,217 x 100%
= 3.07%

• Selling Price and Buying Price

Find the selling price or purchase price if profit or loss is known
Selling price :

Selling price = buying price + profit
Selling price = buying price – loss

Purchase price :

Purchase price = selling price – profit
Purchase price = selling price + loss

Example:
Mr. Amat sells the house with a 15% profit. Initially he bought the house for IDR 300,000,000. Calculate the selling price?
Answer:
Profit percentage = (Sales price – Purchase price)/ Purchase price x 100%
15% = (Sales price – 300,000,000) / 300,000,000 x 100%
Sales price = (15% x 300,000,000) + 300,000,000
= 45.000.000 + 300.000.000
= IDR 345,000,000

• Discount or Rebate

Discounts or rebates are price discounts given by traders or producers to buyers or consumers.

Price paid = original price – discount
Discounts are generally expressed in percent

% Discount = (amount of discount) / (original price) × 100%

Example:
In a mall it says a 30% discount for bags with an initial price of IDR 180,000. So how much is the bag after getting the discount?
Answer:
Bag price after discount = IDR 180,000 – (30% x IDR 180,000)
= IDR 126,000

• Gross, Tara and Net

Gross is the gross weight consisting of the net weight of the goods (net) and the weight of the packaging (tara).

Gross = net + tare

Net is the net weight obtained from the gross (gross) weight minus tare

net = gross – tare

The tare value is generally expressed in percent

% Tara= (tare amount)/gross×100%

• Taxes and Savings Interest

If the amount of money saved initially is M, the bank pays a single interest of p% per year, and saves for t years, then

Interest for 1 year = M×p%
Interest for t years = M×p%×t
Interest for t months = M×p/12%×t
total savings = M + interest

Tax is a mandatory contribution from the community to the state based on the law by not reciprocating services directly used to finance general expenditures to improve welfare public.

Example:
Mr. Tomi bought a refrigerator for IDR 2,400,000 and is subject to a 10% Value Added Tax (VAT). How much money should Pak Tomi pay?
Answer:
VAT = 10% x IDR 2,400,000
= IDR 240,000
The price to be paid = IDR 2,400,000 + IDR 240,000
= IDR 2,640,000

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Example questions and solutions

Problem 1.

A bag is purchased for Rp. 200,000.00. The selling price of the bag so that a profit of 35% is….
A IDR 285,000.00
B. IDR 270,000.00
C. IDR 253,000.00
D. IDR 235,000.00
Answer: B
How to smart solutions
Using a percent comparison, because the profit is 35%, the selling price is 135%. Therefore :
selling price = 135/100 × IDR 200,000.00
= IDR 270,000.00

Problem 2.

Half a dozen children's clothes were bought for IDR 450,000.00. If the desired profit is 20%, then the selling price of 1 set of children's clothes is….
A IDR 90,000.00
B. IDR 84,000.00
C. IDR 80,000.00
D. IDR 25,000.00
Answer: A
How to smart solutions
Using the ratio of percent in each unit
Purchase price per set = IDR 450,000.00: 6
= IDR 75,000.00
Because the profit is 20%, the selling price is 120% so
Perset selling price = 120% x IDR 75,000.00
IDR 90,000.00

Problem 3.

A frying pan if sold at IDR 75,000.00 will give a profit of 25%. The purchase price of the frying pan is…
A IDR 50,000.00
B. IDR 60,000.00
C. IDR 93,750.00
D. IDR 100,000.00
Answer: B
How to smart solutions
Use percent comparisons
Purchase price = 100%, selling price = 125%, which is IDR 75,000.00 then:
Purchase price = 100/125 × IDR 75,000.00
= 4/5 × IDR 75,000.00
= IDR 60,000.00

Problem 4.

A used washing machine was bought for IDR 425,000.00. Then it was repaired and cost IDR 175,000.00. If you want 40% profit, then the selling price of the washing machine is….
A IDR 595,000.00
B. IDR 770,000.00
C. IDR 840,000.00
D. IDR 850,000.00
Answer: C
How to smart solutions
Capital = purchase price + repair costs
= IDR 425,000.00 + IDR 175,000.00
= IDR 600,000.00
Selling price = 140% x IDR 600,000.00
= IDR 840,000.00

Problem 5.

A second laptop is repaired at a cost of IDR 200,000.00. If the laptop is sold at Rp. 1,050,000.00, it will provide a profit of 16 2/3%. The purchase price of the laptop is….
A IDR 900,000.00
B. IDR 850,000.00
C. IDR 750,000.00
D. IDR 700,000.00
Answer: D
How to smart solutions
Purchase price = Capital – repair costs
= (100%)/(116 2/3%)×Rp 1,050,000.00 – Rp 200,000.00
= 6/7×Rp 1,050,000.00 – Rp 200,000.00
= Rp. 900,000.00-Rp. 200,000.00
= IDR 700,000.00

Problem 6.

It is known that the price of a pair of shoes is IDR 68,000.00. The price of a pair of shoes after 25% discount is...
A IDR 51,000.00
B. IDR 53,000.00
C. IDR 57,000.00
D. IDR 85,000.00
Answer: A
How to smart solutions
Price paid = 75% × original price
= ¾ × IDR 68,000.00
= IDR 51,000.00

Problem 7.

The price of a shirt after a 15% discount is IDR 102,000.00. The price of the shirt before the discount is….
A IDR 110,000.00
B. IDR 120,000.00
C. IDR 125,000.00
D. IDR 140,000.00
Answer: B
How to smart solutions
Because of the 15% discount, the price after the 100% – 15% discount = 85% is IDR 102,000.00..
Price before discount = (100%)/(85%) × IDR 102,000.00
= 20/17 × IDR 102,000.00
= IDR 120,000.00

Problem 8.

The gross of one sack of fertilizer is 48 kg. if the rate is 2.5%, then the nett of one sack of fertilizer is….
A 46.8 kg
B. 46.2 kg
C. 42.8 kg
D. 42.6 kg
Answer: A
How to smart solutions
% net = 100% – 2.5% = 97.5%
So that :
Net = 97.5% × 48 kg
= 46.8 kg

Problem 9.

Abi saved Rp. 300,000.00 in a bank. After 5 months he gets Rp. 18,750.00 in interest. If Bima wants to save Rp. 500,000.00 at the same bank, the amount of interest Bima will receive after 6 months of saving is...
A IDR 27,500.00
B. IDR 35,700.00
C. IDR 37,500.00
D. IDR 53,700.00
Answer: C
How to smart solutions

Bima's savings interest for 6 months = M_Bima/M_Abi × t_Bima/t_Abi × Andi's savings interest
= (Rp 500,000.00)/( Rp. 300,00.00) × 6/5×Rp 18,750.00
= 2 × IDR 18,750.00
= IDR 37,500,,00

Problem 10.

Ibnu has a loan of Rp. 600,000.00 at a bank and will be paid in installments every month for 4 months. If the interest on the loan is 18% per year, then the amount of installments per month is...
A IDR 156,000.00
B. IDR 159,000.00
C. IDR 165,000.00
D. IDR 186,000.00
Answer: B
How to smart solutions
Monthly installment amount = M/t + 1 month interest
= (IDR 600,000.00)/4 + IDR 600,000.00 × (18%)/12
= IDR 150,000.00 + IDR 9000.00
= IDR 159,000.00

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