Unitary Method Questions

• Unitary method (direct proportion): If 20 articles cost ₹ 90, what is the cost of 9 articles?
• Unitary method: If 24 oranges cost ₹ 72, find the cost of 120 oranges (assume a constant rate).
• Unitary method: If 12 pens cost ₹ 84, what is the cost of 10 such pens?
• Unitary method with dozens: If 15 eggs cost ₹ 75, find the cost of 4 dozen eggs (48 eggs).
• Unitary method (reverse count): If 16 dozens of bananas cost ₹ 360, how many bananas can be bought for ₹ 60?
• Unitary method application on constant-rate production: A worker makes one toy every 2 hours at a steady, uniform rate. If he continues working at the same speed for a total of 80 hours, how many complete toys will he manufacture in that period?
• Direct proportion for uniform material: If 45 m of a uniform rod weighs 171 kg, what will be the weight (in kilograms) of 12 m of the same rod, assuming the rod has constant density and cross-section throughout its length?
• Scaling running distance with constant pace: In a race scenario, Ravi covers 5 km in 20 minutes at a steady pace. Assuming he keeps the same speed, how much distance (in kilometers) will he cover in 100 minutes?
• Similar triangles with shadows (height–shadow proportion): A tree is 12 m tall and casts an 8 m long shadow at a given time. At the same time and under the same sun angle, a flagpole casts a 100 m long shadow. Using direct proportion of height to shadow length, what is the height of the flagpole?
• Symbolic unitary method (wire pricing at a constant rate): If the cost of x meters of wire is d rupees at a fixed rate, what is the cost (in rupees) of y meters of the same wire at that identical rate? Express the answer in terms of x, y, and d.
• Consumption rate of fodder per cow: In a dairy farm, 40 cows consume 40 bags of husk in 40 days at a steady rate. Based on this, in how many days will one cow consume one full bag of husk?
• Cow–goat equivalence in feed consumption: If 21 goats eat as much as 15 cows (same period and same feed), then how many goats will consume as much as 35 cows under identical conditions?
• Work-rate with persons and hours changed: Thirty-nine persons can repair a road in 12 days when they work 5 hours each day. If thirty persons work 6 hours each day at the same efficiency, in how many days will they complete the same work?
• Output scaling with workers and days: Four mat-weavers weave 4 mats in 4 days at a constant rate. At this same rate, how many mats would 8 mat-weavers weave in 8 days?
• Price–weight proportion with grams and paise: If a quarter kilogram (250 g) of potatoes costs 60 paise at a constant rate, how many paise will 200 g of potatoes cost at the same price per gram?
• Single-cow consumption time from group usage: In a dairy farm, 40 cows eat 40 bags of husk in 40 days at a steady rate. Based on this information, in how many days will one cow consume exactly one bag of husk?
• Time to weave a fixed length at a constant per-second rate: An industrial loom weaves 0.128 meters of cloth every second at a steady rate. Approximately how many seconds are required for the loom to weave 25 meters of cloth in total?
• Scaling harvested area with men and days: If 8 men can reap 80 hectares in 24 days at a constant rate, then how many hectares can 36 men reap in 30 days under similar conditions?
• Symbolic pricing at a constant rate (clean algebraic form): If the cost of x meters of wire is d rupees, determine the cost of y meters of wire at the same rate. Provide a simplified algebraic expression.
• Direct proportion: pricing toys by quantity at a constant rate: If the price of 23 toys is ₹ 276 at a uniform per-toy price, what will be the total price (in rupees) of 12 toys at the same rate?