# The Ratio 2x:3y Equals To :

If (x^{3}-y³):(x^{2}+xy+y^{2})=5:1 and (x^{2}-y^{2}):(x-y)=7:1, the ratio 2x:3y equals

- 4:1
- 3:2
- 2:3
- 4:3

**Answer: (1) 4: 1**

**Explanation:-
**(x

^{3}– y

^{3}): (x

^{2}+ xy + y

^{2}) = 5: 1

(x – y) (x

^{2}+ y

^{2}+ xy)/ (x

^{2}+ y

^{2}+ xy) = 5/1

(x – y)/1 = 5/1

x – y = 5 ………………………… (1)

And

(x^{2} – y^{2}): (x –y) = 7: 1

(x – y) (x + y)/(x – y) = 7/1

(x + y)/1 = 7/1

x + y = 7 ………………………….. (2)

Add equation (1) & (2),

x – y + x + y = 5 + 7

2 x = 12

Then, x = 12/2 => x = 6

Put the value of x in equation (1),

Then, 6 – y = 5

– y = 5 – 6

– y = – 1

y = 1

Then, the value of 3 y = 3 x 1

3 y = 3

Therefore, 2x/3y = 12/3

2x/3y = 4/1

Then, the ratio 2x: 3y = 4: 1

Hence, the answer is (1) 4: 1.