If 3 is added to both the numerator and the denominator of a fraction, it becomes 5/7. If 6 is subtracted from both the numerator and the denominator, it becomes 1/2. What is the fraction?a)15/21b)12/18c)18/32d)10/17Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Let the fraction be x/y.

According to the question

(x + 3)/(y + 3) = 5/7 .... (i) and

(x - 6)/(y - 6) = 1/2 ..... (ii)

From equation (i) we get

7x + 21 = 5y + 15

7x - 5y = - 6 .... (iii)

From equation (ii) we get

2x - 12 = y - 6

2x - y = 6

10x - 5y = 30 .... (iv)

Subtracting (iii) from (iv) we get

3x = 36

x = 12

Use x = 12 in equation (iv) we get

y = 18

Hence, fraction = x/y = 12/18

Answer

Given Information:
- After adding 3 to both the numerator and the denominator, the fraction becomes 5/7.
- After subtracting 6 from both the numerator and the denominator, the fraction becomes 1/2.

Let's assume the fraction to be x/y.

Step 1: Formulating the equations:
- Adding 3 to both the numerator and the denominator:
(x + 3) / (y + 3) = 5/7 ----(1)

- Subtracting 6 from both the numerator and the denominator:
(x - 6) / (y - 6) = 1/2 ----(2)

Step 2: Solving the equations:

Solving equation (1):
Cross multiplying, we get:
7(x + 3) = 5(y + 3)
7x + 21 = 5y + 15
7x - 5y = 15 - 21
7x - 5y = -6 ----(3)

Solving equation (2):
Cross multiplying, we get:
2(x - 6) = y - 6
2x - 12 = y - 6
2x - y = -6 + 12
2x - y = 6 ----(4)

Step 3: Solving the simultaneous equations:
Multiplying equation (4) by 5 and equation (3) by 2, we get:
10x - 5y = 30 ----(5)
14x - 10y = -12 ----(6)

Multiplying equation (5) by 2 and equation (6) by 5, we get:
20x - 10y = 60 ----(7)
70x - 50y = -60 ----(8)

Subtracting equation (7) from equation (8), we get:
50x = -120
x = -120/50
x = -12/5

Substituting the value of x in equation (4), we get:
2(-12/5) - y = 6
-24/5 - y = 6
-24 - 5y = 30
-5y = 30 + 24
-5y = 54
y = 54/(-5)
y = -54/5

Therefore, the fraction is -12/5 divided by -54/5, which simplifies to 12/18.

Hence, the correct answer is option B) 12/18.

Similar CAT Doubts

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In a given fraction, if you add 4 to the numerator and 5 to the denominator, the fraction becomes 1. If you multiply the numerator by 2 and denominator by 3, the fraction becomes 4/5. What is the original fraction?

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