Question

The areas of three flats A, B and C are in the
ratio 5:6 : 8 respectively. If the difference in
the area of flat C and flat A is 270 square metres,
what is the area of flat B in square metres ?​

Answer 1

Given :-

The areas of 3 flats A , B and C are in the ratio of 5 : 6 : 8 .

The difference in the areas of flat C and flat A is 270 m²

Required to find :-

• Area of flat B in m² ?

Solution :-

Given data :-

The areas of 3 flats A , B , C are in the ratio of 5 : 6 : 8

The difference in the areas of the flat C and flat A is 270 m²

we need to find the area of flat B in m² .

Given ratio of the areas is ;

5 : 6 : 8

Let,

The area of the flat A be 5x

area of the flat B be 6x

area of the flat C be 8x

( where X is any positive integer )

According to problem ;

The difference between the areas of flat C and flat A is 270 m²

This implies,

8x - 5x = 270 m²

This is because,

we considered the area of flat A and flat C as 5x & 6x respectively .

By solving future we get ;

=> 8x - 5x = 270 m²

=> 3x = 270 m²

=> x = 270 m²/3

=> x = 90 m²

Hence,

• value of x is 90 m²

So,

Area of the flat A = 5x = 5 ( 90 m² ) = 450 m²

Area of the flat B = 6x = 6 ( 90 m² ) = 540 m²

Area of the flat C = 8x = 8 ( 90 m² ) = 720 m²

Therefore,

Area of the flat B ( in m² ) = 540 m²

Verification :-

Now, let's verify whether our calculations are correct or not . For that, let's consider the one of the statement given in the question .

The statement is ;

The difference between the areas of flat C and flat A is 270 m²

This implies,

( Area of flat A = 450 m² )

( Are of flat C = 720 m² )

720 m² - 450 m² = 270 m²

270 m² = 270 m²

LHS = RHS

Hence verified

Answer 2

$\bigstar\rm\blue{GIVEN}\bigstar$

• The Area of three flats A,B,C are in the Ratio 5:6:8 respectively.

• If the difference in the area of Flat C and Flat A is 270m²......eq 1

$\bigstar\rm\blue{TO\:FIND}\bigstar$

• The area of Flat B in m²

Now, Atq.

$\implies\rm\blue{Let\:the\:ratio\:be\:x}$

Area of flat A= 5x

Area of Flat B= 6x

Area of flat C= 8x

Atq.

$\implies\rm\red{8x-5x=6x}$

$\implies\rm\red{3x=270}$......using eq 1

$\implies\rm\red{x=\dfrac{\cancel{270}}{\cancel{3}}}$

$\implies\rm\red{x=90m^2}$

Put the value of x

Area of Flat A= 450m²

Area of Flat C = 720m²

Area of Flat B= 6×90= 540m².

Now, Let's Check it.

Area of Flat C- Area of Flat A= 270m²

$\implies\bf{720-450=270}$

Hence, ✔️Verfied.