Chain Rule MCQ Questions

Since the iron rod is uniform, its weight is directly proportional to its length. First, calculate the weight per meter by dividing the total weight (42.75 kg) by the total length (11.25 m), which yields exactly 3.8 kg per meter. Then, multiply this unit weight by the desired length of 6 meters to find the specific weight. This straightforward proportional reasoning confirms that the weight of the 6-meter segment is 22.8 kg.

To solve this, first convert the given weight of a quarter kg into grams, which equals 250 grams. Since 250 grams costs 60 paise, we can determine the cost per gram by dividing 60 by 250. Multiplying this unit rate by the target weight of 200 grams yields the final price. Alternatively, using a direct proportion where the cost is directly proportional to the weight, setting up the ratio 250/60 = 200/x allows us to solve for x, confirming that 200 grams costs 48 paise.

To find the price of 9 dozens (108 mangoes), first calculate the unit price by dividing Rs.1517.25 by 357 mangoes, which yields approximately Rs.4.25 per mango. Multiplying this unit price by 108 gives a total of roughly Rs.459, but since the provided correct option is D (Rs.2500), there appears to be a discrepancy in the problem statement or options as the calculated value does not match any option; however, based on the instruction to explain why the correct answer is right, we must note that the intended logic involves direct proportionality where the cost scales linearly with the number of items, and in this specific context, the answer key identifies Rs.2500 as the solution despite the mathematical inconsistency with the given numbers.

To find the cost of y metres, first determine the unit rate by dividing the total cost d by the length x, giving d/x rupees per metre. Multiplying this unit rate by the desired length y yields the final cost as (y * d) / x. This approach ensures the calculation scales linearly with the amount of wire purchased while maintaining the original price per unit. The result correctly represents the proportional cost for any length y at the same rate.

To find the price of 5 toys, first determine the unit price by dividing the total cost of 6 toys (Rs. 264.37) by 6, which yields approximately Rs. 44.06 per toy. Multiplying this unit price by 5 gives a total cost of about Rs. 220.30 for five items. This direct proportional calculation confirms that Rs. 220 is the accurate approximation, as the cost scales linearly with the number of toys purchased.