Ram is taller than Shyam by 10%. By what percent Shyam is shorter than Ram

Questions : Ram is taller than Shyam by 10%. By what percent Shyam is shorter than Ram?

Answer:  

Shortcut Formula:

$$\text{Percentage Decrease} = \frac{\text{Percentage Increase} \times 100}{\text{Percentage Increase} + 100}$$

Given:

• Ram is 10% taller than Shyam

Applying the formula:

$$\text{Percentage Decrease} = \frac{10 \times 100}{10 + 100}$$ $$= \frac{1000}{110} \approx 9.09\%$$

Final Answer:

Shyam is approximately 9.09% shorter than Ram.

Alternative 

Here's how to solve this:

1. Assume a Baseline

Let Shyam's height be 100 (it's easier to work with percentages).

2. Calculate Ram's Height

Ram is 10% taller than Shyam, so Ram's height is 100 + (10% of 100) = 100 + 10 = 110.

3. Find the Difference in Height

The difference in height between Ram and Shyam is 110 - 100 = 10.

4. Calculate the Percentage Difference (relative to Ram's height)

Shyam is shorter than Ram by 10. To find the percentage by which Shyam is shorter than Ram, we need to express this difference as a percentage of Ram's height:

(Difference in height / Ram's height) * 100 = (10 / 110) * 100 ≈ 9.09%

Answer: Shyam is approximately 9.09% shorter than Ram.

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