RS Aggarwal Class 7 Mathematics Solutions Chapter 9 Unitary Method

Question 1. Cost of 15 oranges is Rs 110. What is the cost of 39 oranges?
Answer: The cost of 1 orange is Rs 110/15. Therefore, the cost of 39 oranges = (110/15) × 39 = Rs 286.
In simple words: Find what one orange costs, then multiply that amount by 39 to get the total cost.

Exam Tip: Always find the unit cost first (cost per item), then multiply by the required quantity - this is the essence of the unitary method.

Question 2. Amount of sugar bought for Rs 260 is 8 kg. How much sugar can be bought for Rs 877.50?
Answer: The amount of sugar obtained for Rs 1 = 8/260 kg. Therefore, the amount of sugar that can be purchased for Rs 877.50 = (8/260) × 877.50 = 27 kg.
In simple words: Find how much sugar costs one rupee, then multiply that by 877.50 to find the total quantity.

Exam Tip: This is an inverse unitary method problem - you start with quantity and find cost, so reverse the fraction carefully.

Question 3. Length of silk purchased for Rs 6290 is 37 m. What length of silk can be purchased for Rs 4,420?
Answer: The length of silk obtained for Rs 1 = 37/6290 m. Therefore, the length of silk that can be bought for Rs 4,420 = (37/6290) × 4420 = 26 m.
In simple words: Calculate how much silk you get per rupee, then multiply by the new amount of money to find the new length.

Exam Tip: Always set up the proportion carefully - keep the same units (price with price, length with length) on opposite sides of the proportion.

Question 4. A worker is paid Rs 1,110 for 6 days of work. How many days did the worker work if paid Rs 4625?
Answer: The payment received per day = 1,110 ÷ 6 days. Therefore, the number of days worked = 4625 ÷ (1,110/6) = (6/1,110) × 4625 = 25 days. The worker completed 25 days of work in a month.
In simple words: First find how much is earned each day, then divide the total payment by the daily wage to find the number of days.

Exam Tip: Watch for the direction of the question - if asking for quantity instead of cost (or days instead of payment), invert your ratio accordingly.

Question 5. A car travels 357 km using 42 litres of petrol. How far will it travel with 12 litres of petrol?
Answer: The distance covered per litre of petrol = 357/42 km. With less petrol, the car travels less distance. Therefore, distance travelled with 12 litres = (357/42) × 12 = 102 km.
In simple words: Calculate how many kilometres the car covers using one litre, then multiply by 12 to find the distance for 12 litres.

Exam Tip: Recognise direct proportion problems - when one quantity increases, the other increases too (more petrol means more distance).

Question 6. The train fare for a journey of 900 km is Rs 2520. What is the fare for a journey of 360 km?
Answer: The cost of travelling 1 km by train = Rs 2520/900. Therefore, the cost of travelling 360 km by train = (2520/900) × 360 = Rs 1008. The train fare for a journey of distance 360 km is Rs 1,008.
In simple words: Find the cost per kilometre, then multiply that by 360 to get the total fare for the shorter journey.

Exam Tip: Check if your answer is sensible - a shorter journey should cost less money than a longer journey.

Question 7. A train takes 45 minutes to cover a distance of 51 km. How long will it take to cover a distance of 221 km?
Answer: The time required to cover a distance of 1 km = 45/51 minutes. Therefore, time needed to cover 221 km = (45/51) × 221 = 195 minutes = 3 hours 15 minutes. The train will need 3 hours 15 minutes to travel 221 km.
In simple words: Calculate how many minutes it takes to travel 1 km, then multiply by 221 to find the total time needed.

Exam Tip: Remember to convert the final answer to a more practical form (hours and minutes) rather than leaving it in large numbers of minutes.

Question 8. An iron rod that weighs 85.5 kg has a length of 22.5 m. What is the length of an iron rod that weighs 22.8 kg?
Answer: The length of an iron rod weighing 1 kg = 22.5/85.5 m. Therefore, the length of an iron rod weighing 22.8 kg = (22.5/85.5) × 22.8 = 6 m.
In simple words: Find the length that corresponds to 1 kg of weight, then multiply by 22.8 to find the length for the heavier rod.

Exam Tip: In unitary method, the direction of proportion matters - directly proportional relationships increase together, inverse relationships move opposite ways.

Question 9. Number of paper sheets weighing 162 g is 6. How many sheets will weigh 13.5 kg?
Answer: The number of sheets weighing 1 g = 6/162. Therefore, the number of sheets that will weigh 13.5 kg = (6/162) × 13.5 × 1000 = 500 sheets.
In simple words: Calculate how many sheets weigh 1 gram, then multiply by the total number of grams in 13.5 kg to find the total sheets needed.

Exam Tip: Always convert all measurements to the same units before applying the unitary method - here, convert 13.5 kg to grams first.

Question 10. Number of cartons needed to pack 1152 soap bars is 8. How many cartons are needed to pack 3888 soap bars?
Answer: The number of cartons required to pack 1 soap bar = 8/1152. Therefore, the number of cartons needed to pack 3888 soap bars = (8/1152) × 3888 = 27 cartons. Thus, 27 cartons are required to pack 3888 soap bars.
In simple words: Find how many cartons are needed for just 1 bar of soap, then multiply by 3888 to get the total number of cartons needed.

Exam Tip: Simplify the fraction before multiplying to avoid working with large numbers - this saves time and reduces calculation errors.

Question 11. A pile has a thickness of 44 mm when it contains 16 cardboards. How many cardboards will be in a pile of thickness 71.5 cm?
Answer: The number of cardboards in a pile of thickness 1 mm = 16/44. Therefore, the number of cardboards in a pile of thickness 71.5 cm = (16/44) × 71.5 × 10 = 260 cardboards (since 1 cm = 10 mm). Thus, 260 cardboards will be present in a pile of thickness 71.5 cm.
In simple words: Find how many cardboards fit in 1 mm of thickness, then multiply by 715 mm (which is 71.5 cm) to get the total number of cardboards.

Exam Tip: Watch your unit conversions carefully - converting between cm and mm (or other units) is crucial to getting the right answer.

Question 12. A flagstaff casts a shadow of length 8.2 m, and at the same time, a building casts a shadow of length 1 m. If the building is 20.5 m tall, what is the height of the flagstaff?
Answer: The height of the building that casts a shadow of length 1 m = 20.5/1 m. Therefore, the height of the flagstaff that casts a shadow of length 8.2 m = (20.5/1) × 8.2 = 17.5 m. The height of the required building is 17.5 m.
In simple words: When shadows are cast at the same time, they follow the same proportion - taller objects have longer shadows, shorter objects have shorter shadows.

Exam Tip: This type of problem uses the property that shadow length is directly proportional to object height when the sun is at the same angle for both objects.

Question 13. It takes 15 workers to build a wall 16.25 m long in one day. How many workers should be employed to build a wall 26 m long in the same time?
Answer: The number of workers required to build a wall of length 1 m = 15/16.25. Therefore, the number of workers that should be recruited to build a wall of length 26 m = (15/16.25) × 26 = 24 workers. Thus, 24 workers should be engaged to construct a wall of length 26 m in a day.
In simple words: More workers are needed for longer walls - divide the total workers by the wall length to find workers per metre, then multiply by the new wall length.

Exam Tip: Here, the time period is fixed (one day), so focus only on the relationship between wall length and number of workers required.

Question 14. A hospital can accommodate 60 patients with a monthly milk ration of 1350 litres. If the monthly ration is increased to 1710 litres, how many more patients can be accommodated in the hospital?
Answer: The number of patients who can receive care with 1 litre of milk = 60/1350. Therefore, the number of patients who can receive care with 1710 litres of milk = (60/1350) × 1710 = 76 patients. Hence, 76 patients can be accommodated in the hospital if the monthly ration of milk is raised to 1710 litres.
In simple words: More milk means more patients can be served - find how many patients one litre supports, then multiply by the new amount of milk.

Exam Tip: Read carefully - the question asks how many MORE patients can be accommodated, so you may need to subtract the original number from the new number if that is what is being asked.

Question 15. A spring extends 2.8 cm under a weight of 150 g. What weight will produce an extension of 19.6 cm?
Answer: The weight that would generate an extension of 1 cm = 150/2.8 g. Therefore, the weight that would generate an extension of 19.6 cm = (150/2.8) × 19.6 = 1050 g = 1 kg 50 g.
In simple words: Springs stretch more with heavier weights - find how much weight produces 1 cm of stretch, then multiply by 19.6 to find the weight needed for 19.6 cm of stretch.

Exam Tip: Remember to convert your final answer into appropriate units (grams to kilograms and grams) if the result is large - this makes the answer clearer and more practical.