Question

A rectangular garden is 276 m long and 180 m wide. It has an inside path of uniform width of 3 m all around it. Find the cost of

1. repairing the path at 10 paise per sq. m and
2. watering the remaining portion of the garden at ₹ 3 per 100 sq. meters.

Answer 1

Given: A rectangular garden 276 m by 180 m with an inside path of uniform width 3 m all around.

Step-wise calculation:

1. Area of whole garden (outer rectangle)

= 276 × 180

= 49,680 m²

2. Inner garden (after removing path):

Each dimension reduced by 2 × 3 = 6 m 

Inner length

= 276 – 6 

= 270 m 

Inner width

= 180 – 6 

= 174 m 

Area of inner garden

= 270 × 174 

= 46,980 m²

3. Area of the path

= Area outer – Area inner

= 49,680 – 46,980

= 2,700 m²

4. Cost to repair the path at 10 paise per m² 10 paise = ₹ 0.10. 

Cost = 2,700 × 0.10

= ₹ 270.00.

5. Cost to water the remaining portion (inner garden) at ₹ 3 per 100 m².

Rate per m² = ₹ `3/100`

= ₹ 0.03

Area to water = 46,980 m². 

Cost = 46,980 × 0.03 = ₹ 1,409.40.

i. Cost of repairing the path = ₹ 270.00. 

ii. Cost of watering the remaining portion = ₹ 1,409.40.