Question

What will be the sum of two numbers?
I. Among the two numbers, the bigger number is greater than the smaller number by 6.
II. 40 % of the smaller number is equal to 30 % of the bigger number.
III. The ratio of half of the bigger number to one third of the smaller number is 2 : 1.

• A. I or II
• B. II or III
• C. I and II or I and III
• D. Any two of the three

Answer 1

The Correct Option is C

To determine the sum of two numbers, we will analyze the given statements and see which combinations can solve the problem.

Statement I: Among the two numbers, the bigger number is greater than the smaller number by 6. Let's denote the smaller number as x and the bigger number as y. We have:
y = x + 6.

Statement II: 40% of the smaller number is equal to 30% of the bigger number. This can be expressed as:
0.4x = 0.3y.

Statement III: The ratio of half of the bigger number to one third of the smaller number is 2:1. This translates to:
(1/2)y / (1/3)x = 2/1.

We will analyze combinations of these statements:

I and II:
From Statement I: y = x + 6.
From Statement II: 0.4x = 0.3y.
Plugging y = x + 6 into 0.3y, we have:
0.4x = 0.3(x + 6).
This simplifies to x = 9.
Substituting back, y = 15.
The sum is x + y = 9 + 15 = 24.

I and III:
From Statement I: y = x + 6.
From Statement III: (1/2)y / (1/3)x = 2/1.
Solve the equation: (1/2)(x + 6) / (1/3)x = 2/1.
Simplify to: 3(x + 6) = 4x.
Solving gives x = 18.
Substitute back: y = 24.
The sum is x + y = 18 + 24 = 42.

Conclusion:
I and II provide a consistent solution of sum = 24.
I and III provide another consistent solution of sum = 42.
Therefore, I and II or I and III can provide the sum of the two numbers.