Bissoy.com
Doctors Medicines MCQs Q&A

In a rectangular plot of dimensions 60 m × 35 m, four houses (shaded region) were built leaving pathways, as shown in the figure given below. If area of shaded region is 36% of the area of rectangular park, then find the value of x. 

In a rectangular plot of dimensions 60 m × 35 m, four houses (shaded region) were built leaving pathways, as shown in the figure given below. If area of shaded region is 36% of the area of rectangular park, then find the value of x.  Correct Answer 8 m

Given:

Formula used:

Area of rectangle = length × breadth

Calculation:

Area of rectangular plot = 60 × 35 = 2100 m2 

When the houses are built, 

⇒ Length of shaded region = (60 – 4x) m 

⇒ Breadth of shaded region = (35 – x) m 

⇒ Area of shaded region = (60 – 4x) (35 – x) = (2100 – 200x + 4x2) 

Now, area of shaded region = 36% of Area of rectangular plot 

⇒ (2100 – 200x + 4x2) = 36% of 2100 

⇒ 2100 – 200x + 4x2 = 756 

⇒ 4x2 – 200x + 1344 = 0 

⇒ x2 – 50x + 336 = 0 

⇒ x2 – 8x – 42x + 336 = 0 

⇒ (x – 8) (x – 42) = 0 

⇒ x = 8, 42 

∵ The value of ‘x’ cannot be greater than the breadth of park 

∴ x = 8 m 

Related Questions

The selling price of plot is directly proportional to the square of area of plot in m2. If the cost price of square shaped plot is Rs. 50000 and the profit percent of a dealer is 25% on selling square shaped plot then find the cost price of rectangular shaped plot if the dealer gains 50% on selling of rectangular plot where the length and breadth of rectangular plot is 30 m and 20 m while the side length of square plot is 20 m.
In a rectangular park of dimensions 40 m × 20 m, a pathway of width ‘x’ m is built as shown in the figure given below. If the ratio of the area of shaded region to the area of rectangular park is 16 ∶ 25 then find the value of x.
A big rectangular plot of area 4320 m2 is divided into 3 square-shaped smaller plots by fencing parallel to the smaller side of the plot. However some area of land was still left as a square could not be formed. So, 3 more square-shaped plots were formed by fencing parallel to the longer side of the original plot such that no area of the plot was left surplus. What are the dimensions of the original plot ?
A rectangular plot has a concrete path running in the middle of the plot parallel to the breadth of the plot. The rest of the plot is used as a lawn which has an area of 420 sq. m. If the width of the path is 4 m and the length of the plot is greater than its breadth by 36 m, what is the area of the rectangular plot? 
The structure of houses in rural area is linked to the climatic conditions in which they are built. There is a village where houses have following features: Houses are made on strong bamboo pillars. Inside of houses is also made of wood. Houses are made almost 3 m to 3.5 m above the ground. Roofs are made with a slope. If in this village it rains heavily, the village should be part of
In a street, there are certain number of houses. People in that street are decided to paint their houses with certain colours. If four houses are painted with each colour, then one house will be left without any colour. If five houses are painted with each colour, then one colour will remain. Find the number of houses in that street ?
A man had a rectangular plot with dimensions 40 m × 15 m and a triangular plot with sides 10 m, 12 m and 6 m. He paid Rs. 2250 for the ploughing of his rectangular plot. How much money is required for the ploughing of triangular plot at the same rate?
Among eight houses A, B, C, D, E, F, G and H, four houses are situated at the corners of a square - shaped garden. The remaining four houses are situated in the middle of each side of the square. All houses face the centre of the square. B is between A and H. F is to the immediate left of G. D is to immediate left of C, which is to the immediate left of F. B and F are in the middle of the two sides facing each other. D is not adjacent to H. Which four houses are situated at the corners.
The prices of houses A and B were in the ratio of 2 : 3 and prices of houses B and C were in the ratio 3 : 5 before repairs. A builder spends 10%, 20% and 30% of the original price of the house on repairs for the houses and sells it without any profit. Find the ratio of the prices at which the houses were sold after the repairs were done.
Find the diagonal of a square plot whose area is 600 m2 more than the area of a rectangular plot that has a length and breadth ratio of 5 : 2.  A side of the square plot is 60% larger than the breadth of the rectangular plot.