Answer :

To divide 840 in the ratio [tex]\(3:4\)[/tex], follow these steps:

1. Find the total ratio:
Add the parts of the ratio together. In this case, [tex]\(3 + 4 = 7\)[/tex].

2. Calculate each part's value:
- For the first part of the ratio (3), divide the total amount, 840, by the total ratio, 7. Then multiply by 3.
[tex]\[
\text{First part} = \left(\frac{3}{7}\right) \times 840
\][/tex]
[tex]\[
\text{First part} = 360
\][/tex]

- For the second part of the ratio (4), divide the total amount, 840, by the total ratio, 7. Then multiply by 4.
[tex]\[
\text{Second part} = \left(\frac{4}{7}\right) \times 840
\][/tex]
[tex]\[
\text{Second part} = 480
\][/tex]

3. Verify the result:
The two parts add up to the original amount:
[tex]\[
360 + 480 = 840
\][/tex]

Therefore, dividing 840 in the ratio 3:4 gives us two parts: 360 and 480. Thus, the answer is option B: 360: 480.

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