The cost of a diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1 : 2 : 3 : 4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond.

In what ratio must tea at Rs. 62 per Kg be mixed with tea at Rs. 72 per Kg so that the mixture must be worth Rs. 64.50 per Kg?

Amar, Akbar and Antony decide to go for a cycling race, for which they first have a practice race on a racetrack OR. P and Q are points on the track between O and R such that OP : PQ : QR is 1 : 2 : 3. The ratio of the speeds with which Amar, Akbar and Antony covered the leg OP is 2 :3: 4, while for the leg PQ it is 3 : 4 : 2 and for the leg QR it is 4 : 2 : 3. If the ratio of the speeds with which Amar covered the legs OP, PQ and QR is 2 : 3 : 4, who among Amar, Akbar and Antony completed the practice race first?