Question

A rectangular grassy plot of length 6 m and width
4 m has a gravel path of width 1 m all around it
on inside. Find the cost of gravelling the path at
80 paise per $\mathsf {m}^{2}$.​

Answer 1

Answer:

The cost of gravelling the path is Rs. 12.8

Step-by-step explanation:

Given :

Length of the plot = 6 m

Width of the plot = 4 m

Width of the path = 1 m

Rate of gravelling = 80 paise per.m²

The path runs = inside the plot

To find :

The cost of gravelling the path

Solution :

Area of the path = Area of Original Plot - Area of the smaller plot (plot excluding the path)

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★ Area of Original Plot -

$\longrightarrow$ Length × Breadth

$\longrightarrow$ 6 × 4

$\longrightarrow$ 24 m²

Area of Original Plot = 24 m²

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★ Area of the smaller plot -

Dimensions of the smaller plot -

• Length = 6 - (1 × 2) = 6 - 2 = 4 m
• Breadth = 4 - (1 × 2) = 4 - 2 = 2 m

$\longrightarrow$ Length × Breadth

$\longrightarrow$ 4 × 2

$\longrightarrow$ 8 m²

Area of smaller plot = 8 m²

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★ Area of the path -

$\longrightarrow$ 24 - 8

$\longrightarrow$ 16

Area of the path = 16 m²

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★ Cost of gravelling -

Multiply the rate of gravelling by the area.

$\longrightarrow$ 16 × 80

$\longrightarrow$ 1280

Cost = 1280 paise

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★ Convert into rupees -

$\longrightarrow$ 1280 ÷ 100 .......[100 paise = 1 Rupee]

$\longrightarrow$ 12.8

$\therefore$ The cost of gravelling the path is Rs. 12.8

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{AnSwEr :}}}}}$

Given :

• Length of rectangular plot = 6 m
• Breadth of rectangular plot = 4 m
• Breadth of path = 1 m
• Cost of gravelling = 80 paise/m² = Rs. 0.8 per m²

________________________

To Find :

• Cost of Gravelling

________________________

Solution :

1) Area of Bigger plot

$\large{\boxed{\sf{Area \: = \: L \: \times \: B}}} \\ \\ \implies {\sf{Area \: = \: 6 \: \times \: 4}} \\ \\ \implies {\sf{Area \: = \: 24 \: m^2}}$

$\therefore$ Area of Bigger Plot is 24 m²

$\rule{150}{0.5}$

2) Area of Smaller Plot

• Length = 6 - 2 = 4 m
• Breadth = 4 - 2 = 2 m

$\implies {\sf{Area \: = \: 4 \: \times \: 2}} \\ \\ \implies {\sf{Area \: = \: 8 \: m^2}}$

$\therefore$ Area of Smaller plot is 8 m²

$\rule{150}{0.5}$

3) Area of Path

✯ Area of Path = Area of Bigger Plot - Area of Smaller Plot

$\implies {\sf{Area \: = \: 24 \: - \: 8}} \\ \\ \implies {\sf{Area \: = \: 16 \: m^2}}$

$\therefore$ Area of Path is 16 m²

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Cost of Gravelling :

⇒Cost = Area * Cost per m²

⇒Cost = 16 × 0.8

⇒Cost = 12.8

$\therefore$ Cost of Gravelling is Rs. 12.8