The numerator of a certain fraction is increased by 100% and the denominator is increased by 200%. The new fraction thus farmed is 4/21. What is the original fraction?a)2/7b)3/7c)2/5d)4/7e)None of theseCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Let the fraction be x/y
A/Q,
numerator increased by 100%, i.e, x
and denominator increased be 200%, i.e, 2y
so the fraction is (x+x)/( y+2y)= 4/21
solving this we get ,x/y =2/7

Answer

To solve this problem, we can set up an equation using the given information and then solve for the original fraction.

Let's assume the original fraction is x/y. Then, the numerator is x and the denominator is y.

According to the problem, the numerator is increased by 100% and the denominator is increased by 200%. This means that the new numerator is 2x (100% of x is x, so the new numerator is x + x = 2x) and the new denominator is 3y (200% of y is 2y, so the new denominator is y + 2y = 3y).

We are also given that the new fraction formed is 4/21. This gives us the equation: (2x)/(3y) = 4/21.

To solve for x/y, we can cross-multiply and simplify the equation:

(2x)/(3y) = 4/21
21(2x) = 4(3y)
42x = 12y

Now, we can divide both sides of the equation by 6 to simplify further:

7x = 2y

Since we want the original fraction x/y, we can divide both sides of the equation by y:

(7x)/y = 2

This equation tells us that the original fraction is 7/2, which can be simplified to 3.5.

Therefore, the correct answer is option A) 2/7.

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