What is the cost of a banana?Which two of the following statements together provide sufficient information to answer thequestion?i. 7 mangoes and 9 bananas cost Rs. 14.80ii. 4 mangoes and 8 bananas cost Rs. 11.60iii. 3 mangoes and 7 oranges cost Rs. 9.15iv. 5 bananas, 2 mangoes and 3 oranges cost Rs. 12.65
Correct answer: D. (i) and (ii)
- A. (iii) and (iv)
- B. i and iv
- C. ii and iv
- D. (i) and (ii)
Explanation
To find the cost of a banana, we need to determine the price per banana from the given statements.Let's analyze which two statements together provide sufficient information:i. 7 mangoes and 9 bananas cost Rs. 14.80 ii. 4 mangoes and 8 bananas cost Rs. 11.60 iii. 3 mangoes and 7 oranges cost Rs. 9.15 iv. 5 bananas, 2 mangoes and 3 oranges cost Rs. 12.65 Let's start by expressing the cost equations for statements i and ii in terms of mangoes and bananas:From statement i:\[ 7m + 9b = 14.80 \]From statement ii:\[ 4m + 8b = 11.60 \]Now, we need to eliminate mangoes to find the cost per banana. Let's multiply the equations appropriately to achieve this:Multiply equation ii by 7:\[ 28m + 56b = 81.20 \]Multiply equation i by 4:\[ 28m + 36b = 59.20 \]Now, subtract equation i from the modified equation ii:\[ (28m + 56b) - (28m + 36b) = 81.20 - 59.20 \]\[ 20b = 22 \]\[ b = \frac{22}{20} = 1.1 \]So, the cost of one banana is Rs. 1.10.To verify, substitute \( b = 1.1 \) back into one of the original equations. Using statement ii:\[ 4m + 8 \times 1.1 = 11.60 \]\[ 4m + 8.8 = 11.60 \]\[ 4m = 11.60 - 8.8 \]\[ 4m = 2.8 \]\[ m = \frac{2.8}{4} = 0.70 \]Now, check with statement i:\[ 7 \times 0.70 + 9 \times 1.1 = 14.80 \]\[ 4.90 + 9.90 = 14.80 \]\[ 14.80 = 14.80 \]Everything checks out. Therefore, the cost of a banana is Rs. 1.10, and the two statements that together provide sufficient information to answer the question are i and ii.
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