Proportional Reasoning-2Class 8 Mathematics Case Study Questions

A school canteen prepares fresh idli batter for breakfast. The standard recipe uses rice and urad dal in the ratio $3:1$. To enhance the flavour and texture, the chef adds a small amount of fenugreek seeds and flattened rice (poha). The complete ratio for their special batter is Rice : Urad Dal : Fenugreek : Poha :: $12 : 4 : 1 : 2$. For a large batch required for the weekly breakfast menu, the canteen manager plans to use $36$ kg of rice. The grinding process is also time-dependent. A single industrial grinder can process this entire batch of batter in $6$ hours. To speed up the process for a special event, the manager decides to use multiple grinders of the same capacity.

The Sharma family is planning a road trip from Delhi to Jaipur. They are using a physical map with a Representative Fraction (RF) of $1 : 5,000,000$. On this map, the straight-line distance between Delhi and Jaipur measures $5.4$ cm. The family car gives an average mileage of $15$ km per litre of petrol, and the cost of petrol is ₹96 per litre. For the journey, they plan to travel at an average speed of $60$ km/h. They assume the road distance is the same as the geographical distance and they will not stop during the travel. Remember that $1$ km = $100,000$ cm.

A residential society is constructing a boundary wall. For the foundation, they need a strong concrete mixture. The engineer specifies a mix of cement, sand, and gravel in the ratio $1 : 2 : 4$ by volume. The total volume of concrete mixture required for the project is $140$ cubic metres. The construction work is planned to be completed in $20$ days with a team of $7$ workers. However, due to an approaching monsoon, the society wants to complete the work faster. They are considering hiring more workers to reduce the number of days. It is assumed that all workers work at the same rate.