Explanation:To calculate the interest payable at the end of the year for a sum of ₹19,800 invested at 10% interest per annum, compounded half-yearly, follow these steps:
Given:
– Principal (P): ₹19,800
– Annual Interest Rate (r): 10%
– Compounding Frequency (n): 2 times per year (half-yearly)
– Time (t): 1 year
Step 1: Adjust the Annual Rate for Half-Yearly Compounding
Since the interest is compounded half-yearly, the rate per half-year is:

Step 2: Calculate the Number of Compounding Periods

Step 3: Compute the Amount (A) Using the Compound Interest Formula




A = 21,829.50
Step 4: Determine the Interest Payable
Interest = A – P = 21,829.50 – 19,800 = 2,029.50
However, the options provided are much smaller, suggesting a possible error in the problem or options. Let’s recheck the calculation:
Alternative Approach:
If the interest is only for one compounding period (half-year), then:

But this doesn’t match the options either.
Alternatively, if the interest is compounded half-yearly but only for one half-year, the interest would be ₹990, which still doesn’t align with the given options.
Re-evaluating the Problem:
Given the options are much smaller, it’s possible the question is asking for the additional interest earned due to half-yearly compounding compared to simple interest.
Simple Interest for 1 Year:
Simple Interest = P × r × t = 19,800 × 0.10 × 1 = 1,980

#Compound Interest for 1 Year (Half-Yearly):

Compound Interest = 21,829.50 – 19,800 = 2,029.50
Additional Interest Due to Compounding:
2,029.50 – 1,980 = 49.50
But this also doesn’t match the options.
Conclusion:
Given the calculations, the correct total interest payable at the end of the year is ₹2,029.50, but this does not match any of the provided options.
However, if the question is asking for the interest for one half-year only, then:
Interest for 6 months = 19,800 × 0.05 = 990
But this also doesn’t match the options.
Given the discrepancy, the closest option is:

For the purpose of this question, the selected answer is:

Explanation:Let’s find the Median and Mode of the given data set:
—
Given Data Set:
“`
{2.1, 5, 6, 7, 8, 9.3, 11, 15, 17, 19.21, 27, 31, 31, 33, 16.5, 14, 10}
“`
—
✅ Step 1: Arrange in Ascending Order

This gives 17 values, which is odd, so:
—
✅ Step 2: Find Median
Median = middle value of the sorted list
Middle position = item
→ 9th item = 14
So, Median = 14
—
✅ Step 3: Find Mode
Mode = value that appears most frequently
Only 31 appears twice, all others appear once.
→ Mode = 31
—
✅ Step 4: Find Difference

—
✅ Final Answer: 17 ✅
Would you like help with a quick shortcut trick for median and mode difference?