Mixed-fruit purchase (linear Diophantine check): Find how many pineapples were bought. Pineapple costs Rs. 7 each; watermelon costs Rs. 5 each; total spend = Rs. 38. Assume only whole fruits can be purchased; determine the pineapple count. Choose the correct value.

Given data

• Pineapple price = Rs. 7 each.
• Watermelon price = Rs. 5 each.
• Total amount spent = Rs. 38.

Concept/ApproachLet p be pineapples and w be watermelons (integers ≥ 0). Solve the linear Diophantine equation: 7p + 5w = 38.

Step-by-step calculationReduce mod 5: 7p ≡ 38 (mod 5) ⇒ 2p ≡ 3 (mod 5) ⇒ p ≡ 4 (mod 5).Smallest feasible p = 4. Then cost from pineapples = 4 × 7 = 28.Remaining for watermelons = 38 − 28 = 10 ⇒ w = 10 / 5 = 2 (valid integer).

Verification7(4) + 5(2) = 28 + 10 = 38 (matches total).

Final Answer4