RATIO & PROPORTIONS Lecture 08 Venkatesan S IIMB Alumni

So, the general form of such variations will be, A K1+K2 B

The reduction in the speed of a railway engine is directly proportional to the square of the number of bogies attached to it. The speed of the train is 200 kmph when there are 4 bogies and 155 kmph with 5 bogies. What is the maximum number of bogies that can be attached to the train so that it can move? 1. 4 2. 3. 6 5

The reduction in the speed of a railway engine is directly proportional to the square of the number of bogies attached to it. The speed of the train is 200 kmph when there are 4 bogies and 155 kmph with 5 bogies. What is the maximum number of bogies that can be attached to the train so that it can move? 200 K1-K2 (4)2 155 K1 - K2 (5)2 1. 4 2. 3. 6 4. 7 Why? Speed K1 - K2 (x)2 Because, its not a direct variation Question is not saying, Speed but reduction in speed. 5

The reduction in the speed of a railway engine is directly proportional to the square of the number of bogies attached to it. The speed of the train is 200 kmph when there are 4 bogies and 155 kmph with 5 bogies. What is the maximum number of bogies that can be attached to the train so that it can move? 1. 4 2. 3. 6 4. 7 200-K1-K2 (4)2 155 - K1-K2 (5)2 1-2K2 5 K1 280. K1 K2 (x)2 - +ve value. 280-5 (x)2 = +ve value. x2 56 x = 7 (max) 5

The pastry shop sells pastries in boxes of different sizes. The pastries are priced at Rs. 20 per pastry upto 200 pastries. For every additional 20 pastries, the price of the whole lot goes down by Rs.1 per pastry. What would be the number of pastries in the box such that the revenue of the pastry shop from the customer is maximum? 1. 240 2. 280 3. 300 4. None of the above.

The pastry shop sells pastries in boxes of different sizes. The pastries are priced at Rs. 20 per pastry upto 200 pastries. For every additional 20 pastries, the price of the whole lot goes down by Rs.1 per pastry. What would be the number of pastries in the box such that the revenue of the pastry shop from the customer is maximum? 1. 240 2. 280 3. 300 4. None of the above. # Pastries 200 220 240 260 280 300 320 Price Pastry Total 4000 4180 4320 4420 4480 4500 4480 20 19 18 17 16 15 14

The fee (per student in Rs.) charged by Rahul for the "Training" program is inversely proportional to the number of interested students. The normal price is Rs.40 per student if there are 600 students. But for every increase of Rs.1 in the fee, he loses 5 students. What is the maximum amount he can earn?

The fee (per student in Rs.) charged by Rahul for the "Training" program is inversely proportional to the number of interested students. The normal price is Rs.40 per student if there are 600 students. But for every increase of Rs.1 in the fee, he loses 5 students. What is the maximum amount he can earn? Charge 40 50 60 70 80 90 # students 600 550 500 450 400 350 Total 24000 27500 30000 31500 32000 31500

The fee (per student in Rs.) charged by Rahul for the "Training" program is inversely proportional to the number of interested students. The normal price is Rs.40 per student if there are 600 students. But for every increase of Rs.1 in the fee, he loses 5 students. What is the maximum amount he can earn? Charge 40 50 60 70 80 90 79 81 # students 600 550 500 450 400 350 405 395 Total 24000 27500 30000 31500 32000 31500 31995 31995

The duration of the railway journey varies as the distance and inversely as the velocity; the velocity varies directly as the square root of the quantity of the fuel used, and inversely as the number of bogies in the train. In a journey of 50 km in half an hour with 18 bogies, 100 kg fuel is required. How much fuel will be consumed in a journey of 42 km in 28 minutes with 16 bogies? 1. 48 kg 2. 56 kg 3. 64 kg 4. None of the above. Distance 50 Velocity Time oc 0.5-k Velocity V100 10 Distance Velocity18 18 Velocity 50 10 0.5 k 18 0.5 90

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Venkatesan S

IIM Bangalore Alumni | Cleared CAT 2015 | Cleared IIM B, C, L, K & I

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Sadhna yadav

2 years ago

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