Multiple choice

A fruit vendor has one unit each of five different types of fruits: Apples (A1), Bananas (B1), Cherries (C1), Dates (D1), and Elderberries (E1). The prices of A1, B1, and C1 are in the ratio 5 : 6 : 4, while the prices of B1, D1, and E1 are in the ratio 8 : 9 : 10. If D1 costs Rs. 14 more than A1, then what is the total cost (in Rs.) of all the five types of fruits?

  1. Rs. 240

  2. Rs. 270

  3. Rs. 134

  4. Rs. 234

  5. Rs. 284
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D Correct answer
Explanation

From the ratios, A1:B1:C1 = 5:6:4 and B1:D1:E1 = 8:9:10. To combine these, normalize B1 to 24 (the LCM of 6 and 8). Then A1:B1:C1 = 20:24:16 and B1:D1:E1 = 24:27:30. Given D1 - A1 = 14, we have 27x - 20x = 14, so 7x = 14, x = 2. The total sum is (20+24+16+27+30) * 2 = 117 * 2 = 234.

AI explanation

To make the ratio units for B1 equal, find the least common multiple of 6 and 8, which is 24. Multiplying the first ratio by 4 gives A1:B1:C1 = 20:24:16, and multiplying the second ratio by 3 gives B1:D1:E1 = 24:27:30. The combined ratio of the prices of A1, B1, C1, D1, and E1 is 20:24:16:27:30. Since D1 costs Rs. 14 more than A1, the difference of 7 ratio units (27 minus 20) equals 14, making 1 ratio unit equal to Rs. 2. The total cost is the sum of the ratio units (20 + 24 + 16 + 27 + 30 = 117) multiplied by Rs. 2, which gives a total cost of Rs. 234.

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