A mathematics teacher posed the following problems to her students: A. Simrat…
2023
A mathematics teacher posed the following problems to her students:
A. Simrat pays ₹ 60,000 as rent for three months. How much will she have to pay for a whole year if the rent per month remains same?
B. Cost of three dozen bananas is ₹ 45. Calculate the number of bananas that can be purchased for ₹ 12.50.
C. Joey and Jenny are going to school. Joey started walking before Jenny. When Joey was at the third block, Jenny was at the first block. If both are walking with the same speed, then where would Jenny be if Joey is at the ninth block?
Which of the following is correct with respect to the above three questions?
Answer: D. A and B are daily life problems based on unitary method. — Concept The unitary method rests on a single move: divide to find the value for ONE unit, then scale that one-unit value to the number of units asked for. It…
- A.
Only A is based on unitary method.
- B.
B and C are daily life problems based on unitary method.
- C.
A and C are daily life problems based on unitary method.
- D.
A and B are daily life problems based on unitary method.
Attempted by 22 students.
Show answer & explanation
Correct answer: D
Concept
The unitary method rests on a single move: divide to find the value for ONE unit, then scale that one-unit value to the number of units asked for. It is available whenever the two quantities are proportional — directly, when doubling one doubles the other, or inversely, when doubling one halves the other — because in either case one fixed unit value governs the scaling.
What puts a situation outside the method is a relation that is not proportional at all: one in which the two quantities keep a constant DIFFERENCE rather than a constant ratio. There no per-unit value exists to be scaled, and dividing to manufacture one produces a wrong figure. So the test is: does changing the first quantity change the second in a fixed ratio, up or down? If it does, the unitary method applies; if the gap between the two quantities is what stays fixed, it does not.
Application
Rent problem: ₹ 60,000 covers 3 months. Rent for 1 month = 60,000 ÷ 3 = ₹ 20,000. Rent for 12 months = 20,000 × 12 = ₹ 2,40,000. Rent and number of months keep the constant ratio 20,000 per month, so the one-unit value is found and then scaled — the unitary method.
Bananas problem: three dozen = 36 bananas cost ₹ 45. Bananas for ₹ 1 = 36 ÷ 45 = 0.8. Bananas for ₹ 12.50 = 0.8 × 12.50 = 10 bananas. Number of bananas and money keep the constant ratio 0.8 banana per rupee, so again the one-unit value is found and then scaled — the unitary method.
Blocks problem: Joey is at block 3 when Jenny is at block 1, and both walk at the same speed, so Jenny stays a fixed 2 blocks behind Joey throughout: Jenny's block = Joey's block − 2. When Joey is at block 9, Jenny is at 9 − 2 = block 7. Scaling instead would give 9 × (1 ÷ 3) = block 3, which contradicts their equal speeds. What is fixed here is the difference of 2 blocks, not a ratio, so this is not the unitary method.
Cross-check
Problem | Link between the two quantities | Type of relation | Unitary method |
|---|---|---|---|
Rent across months | ₹ 20,000 per month (constant ratio) | Direct proportion | Yes |
Bananas for money | 0.8 banana per rupee (constant ratio) | Direct proportion | Yes |
Jenny's block against Joey's | Jenny = Joey − 2 (constant difference) | Not proportional | No |
Result
The rent problem (A) and the bananas problem (B) are the daily-life problems built on the unitary method, while the walking-blocks problem (C) rests on a constant difference and gives 7, not 3. Hence the correct statement is: A and B are daily life problems based on unitary method.