By how much is `(2)/(3)` rd of 837 less than `(6)/(5)` th of 1200 ?

Options

A. 872
B. 782
C. 882
D. 282

Answer

To solve the problem, we need to find out how much \( \frac{2}{3} \) of 837 is less than \( \frac{6}{5} \) of 1200.

### Step 1: Calculate \( \frac{2}{3} \) of 837
To find \( \frac{2}{3} \) of 837, we multiply 837 by \( \frac{2}{3} \).

\[ \frac{2}{3} \times 837 = \frac{2 \times 837}{3} \]

Calculating the numerator:

\[ 2 \times 837 = 1674 \]

Now divide by 3:

\[ \frac{1674}{3} = 558 \]

So, \( \frac{2}{3} \) of 837 is 558.

### Step 2: Calculate \( \frac{6}{5} \) of 1200
Next, we find \( \frac{6}{5} \) of 1200 by multiplying 1200 by \( \frac{6}{5} \).

\[ \frac{6}{5} \times 1200 = \frac{6 \times 1200}{5} \]

Calculating the numerator:

\[ 6 \times 1200 = 7200 \]

Now divide by 5:

\[ \frac{7200}{5} = 1440 \]

So, \( \frac{6}{5} \) of 1200 is 1440.

### Step 3: Find the difference
Now we need to find out how much \( \frac{2}{3} \) of 837 (which is 558) is less than \( \frac{6}{5} \) of 1200 (which is 1440).

We calculate the difference:

\[ 1440 - 558 = 882 \]

### Final Answer
Thus, \( \frac{2}{3} \) of 837 is 882 less than \( \frac{6}{5} \) of 1200.

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