1. Two cars A and B start from two points P and Q respectively towards each other simultaneously. After travelling some distance, at a point R, car A develops engine trouble. It continues to travel at 2/3rd of its usual speed to meet car B at a point S where PR = QS. If the engine trouble had occurred after car A had travelled double the distance it would have met car B at a point T where ST = SQ/9. Find the ratio of speeds of A and B.2.There are two water drums in my house whose volumes are in the ratio 1 : 5. Every day the smaller drum is filled first and then the same pipe is used to fill the bigger drum. Normally by the time I return from my college i.e. at 1.30 p.m., the smaller drum would just be full. But today I returned a little early and started drawing water from the well with the help of a bucket, poured one-third into the smaller drum and the remaining into the bigger drum. I continued this till the smaller drum was filled. Immediately after that, I shifted the pipe into the bigger drum and went for lunch. Today if the bigger drum was filled in 12 minutes before its normal time, when was the smaller drum full?3.Let Sn denote the sum of the squares of the first n odd natural numbers. If Sn = 533n, find the value of n.
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