Understanding Acre Equivalents and Land Measurement

The question asks us to identify which of the given quantities are exactly equal to one acre. An acre is a standard unit of area used in land measurement, particularly in the imperial and US customary systems. To solve this, we need to know the standard definitions and conversions for an acre in various units.

Defining One Acre

The most common definition of an acre is based on square feet:

• One acre is defined as 43,560 square feet ($\text{sq ft}$).

Let's examine each quantity provided in the options.

Analyzing Quantity A: 43560 sq ft

Quantity A is given as 43,560 sq ft. Based on the standard definition:

• 1 acre = 43,560 sq ft

Therefore, 43,560 sq ft is indeed equal to one acre.

Analyzing Quantity B: 40 gunthas

A guntha is another unit of area used in some regions, particularly in land surveys in parts of India. The conversion between guntha and acre is commonly accepted as:

• 1 acre = 40 gunthas

Therefore, 40 gunthas is equal to one acre.

Analyzing Quantity C: 10 sq gunter's chain

A Gunter's chain is a historical surveying chain, measuring 66 feet. A square Gunter's chain is the area of a square with sides equal to one Gunter's chain.

• Length of 1 Gunter's chain = 66 feet
• Area of 1 square Gunter's chain = $(66 \text{ ft}) \times (66 \text{ ft}) = 4356 \text{ sq ft}$

Now, let's see how many square Gunter's chains make up one acre (43,560 sq ft):

\text{Number of sq gunter's chain in 1 acre} = \frac{\text{Area of 1 acre in sq ft}}{\text{Area of 1 sq gunter's chain in sq ft}} = \frac{43560 \text{ sq ft}}{4356 \text{ sq ft}}

Calculating the division:

\frac{43560}{4356} = 10

So, 1 acre is equal to 10 square Gunter's chains. Therefore, 10 sq gunter's chain is equal to one acre.

Analyzing Quantity D: 4850 sq yds

A yard is equal to 3 feet. A square yard is the area of a square with sides equal to one yard.

• Length of 1 yard = 3 feet
• Area of 1 square yard = $(3 \text{ ft}) \times (3 \text{ ft}) = 9 \text{ sq ft}$

Let's convert one acre (43,560 sq ft) into square yards:

\text{Number of sq yds in 1 acre} = \frac{\text{Area of 1 acre in sq ft}}{\text{Area of 1 sq yd in sq ft}} = \frac{43560 \text{ sq ft}}{9 \text{ sq ft}}

Calculating the division:

\frac{43560}{9} = 4840

So, 1 acre is equal to 4840 square yards. The quantity given is 4850 sq yds, which is not equal to 4840 sq yds. Therefore, 4850 sq yds is not equal to one acre.

Summary of Equivalences to One Acre

Based on our analysis, quantities A, B, and C are each equal to one acre, while quantity D is not.

Selecting the Correct Option

We need to find the option that lists only A, B, and C as being equal to one acre.

• Option 1: Only A, B and C (Matches our findings)
• Option 2: Only A, B and D (Incorrect, D is not equal to 1 acre)
• Option 3: Only B, C and D (Incorrect, D is not equal to 1 acre, and A is equal to 1 acre)
• Option 4: Only A, C and D (Incorrect, D is not equal to 1 acre, and B is equal to 1 acre)

The correct answer is the option that includes A, B, and C only.

Revision Table: Acre Conversions

Additional Information: Understanding Land Area Units

Land area is measured using various units depending on the system (imperial, US customary, metric) and regional traditions. The acre is a historical unit, originally defined as the area a pair of oxen could plough in one day. While 43,560 sq ft is the standard definition in the US and UK, other units like guntha and Gunter's chain relate to older surveying practices.

Understanding these conversions is crucial for real estate, land surveys, and historical context. Units like the rood (1/4 acre) and the furlong (1/8 mile, often defining one side of an acre parcel - 1 furlong by 1 chain) are also related to the acre.

It's important to note that while 40 gunthas is a common equivalence, local variations in land measurement units can exist. However, for the purpose of standard questions like this, these standard conversions are usually assumed.