Mathematics
Writer true (T) or false (F) :
(i) 12 kg apples for ₹ 2160 is a better buy than 15 kg apples for ₹ 2850.
(ii) If 7 men can finish a work in 84 days, then 12 men can finish the same work in 96 days.
(iii) If 9 notebooks cost ₹ 315, then the cost of 20 notebooks is ₹ 700.
(iv) In an indirect proportion, a decrease in one quantity causes an increase in the other quantity.
Unitary Method
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Answer
(i) True
Reason — Compare cost per kg
12 kg for ₹2160:
Cost of 1 kg = 2160 ÷ 12 = ₹ 180 per kg
Now, 15 kg for ₹2850:
Cost of 1 kg = 2850 ÷ 15 = ₹ 190 per kg
Since ₹ 180 is cheaper than ₹ 190, the first option is indeed a better buy.
(ii) False
Reason — Days for 7 men = 84 days
Days for 1 man = (84 x 7) days = 588 days
Days for 12 men = 588 ÷ 12 = 49 days
The statement says 96 days, which is mathematically impossible because increasing the number of men must decrease the time taken.
(iii) True
Reason — Cost of 9 notebook = ₹ 315
Cost of 1 notebook = ₹
Cost of 20 notebooks = ₹ 35 x 20 = ₹ 700 [More notebooks, More cost]
The calculation matches the statement perfectly.
(iv) True
Reason — This is the fundamental definition of Indirect (Inverse) Proportion. As one value goes down, the related value must go up to maintain the constant product (x x y = k).
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Assertion: When x and y are in indirect proportion, then (x + 1) and (y + 1) are also in indirect proportion.
Reason: Two quantities x and y are said to be in indirect proportion, if xy = k, where k is a constant.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
- Assertion (A) is true but Reason (R) is false.
- Assertion (A) is false but Reason (R) is true.