Sum of the length of two trains A and B is 660. The ratio of the speeds of A and B is $5 : 8$. The ratio between the time taken to cross an electric pole by A and B is $4 : 3$. Find the difference in the length of the two trains.

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**Solution:**

1. Let the lengths of trains A and B be $l_1$ and $l_2$ respectively.

2. Given:
   - $l_1 + l_2 = 660$
   - Speed ratio: $\frac{S_A}{S_B} = \frac{5}{8}$, so speeds are $5x$ and $8x$.
   - Time ratio to cross a pole: $\frac{T_A}{T_B} = \frac{4}{3}$, so times are $4y$ and $3y$.

3. Length of a train = speed $\times$ time to cross a pole.

Therefore,
   $$
   l_1 = S_A \times T_A = 5x \times 4y = 20xy
   $$
   $$
   l_2 = S_B \times T_B = 8x \times 3y = 24xy
   $$

4. Sum of lengths:
   $$
   l_1 + l_2 = 20xy + 24xy = 44xy = 660
   $$

So,
   $$
   xy = \frac{660}{44} = 15
   $$

5. Difference in lengths:
   $$
   l_2 - l_1 = 24xy - 20xy = 4xy = 4 \times 15 = 60
   $$

**Answer:** $60$

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