If decreasing 70 by x% yields the same result as increasing 60 by x%, then x% of 91 is :

Options

A. 7
B. 6
C. 8
D. 5

Answer

To solve the problem step by step, we need to set up an equation based on the information given in the question.

### Step 1: Set up the equations
We know that decreasing 70 by x% is the same as increasing 60 by x%.

- Decreasing 70 by x% can be expressed as:
\[ 70 - \frac{x}{100} \times 70 = 70(1 - \frac{x}{100}) \]

- Increasing 60 by x% can be expressed as:
\[ 60 + \frac{x}{100} \times 60 = 60(1 + \frac{x}{100}) \]

Setting these two expressions equal to each other gives us the equation:
\[ 70(1 - \frac{x}{100}) = 60(1 + \frac{x}{100}) \]

### Step 2: Expand both sides
Expanding both sides of the equation:
\[ 70 - \frac{70x}{100} = 60 + \frac{60x}{100} \]

### Step 3: Clear the fractions
To eliminate the fractions, we can multiply the entire equation by 100:
\[ 7000 - 70x = 6000 + 60x \]

### Step 4: Rearrange the equation
Now, we will rearrange the equation to isolate x:
\[ 7000 - 6000 = 60x + 70x \]
\[ 1000 = 130x \]

### Step 5: Solve for x
Now, divide both sides by 130 to find x:
\[ x = \frac{1000}{130} = \frac{100}{13} \]

### Step 6: Find x% of 91
Now we need to find x% of 91:
\[ x\% \text{ of } 91 = \frac{100}{13} \times \frac{91}{100} = \frac{91}{13} \]

### Step 7: Simplify the fraction
Now, we can simplify \(\frac{91}{13}\):
\[ \frac{91}{13} = 7 \]

Thus, the final answer is:
\[ \text{The value of } x\% \text{ of } 91 \text{ is } 7. \]

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