A farmer ordered 15 kg of high-quality seeds and some low-quality seeds. The price of high-quality seeds per kg was three times that of low-quality seeds. Due to a mistake, the quantities of the two types were swapped. This reduced the total cost by 20%. Find the ratio of high-quality seeds to low-quality seeds in the original order.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 11 : 7.
Let price of low-quality seeds = p per kg and high-quality = 3p per kg.
Original total cost = 15 × 3p + x × p = p(45 + x)
Swapped total cost = 15 × p + x × 3p = p(15 + 3x)
Swapped cost = 4/5 of original cost.
p(15 + 3x) = (4/5) × p(45 + x)
⇒ 5(15 + 3x) = 4(45 + x)
⇒ 75 + 15x = 180 + 4x
⇒ 15x − 4x = 180 − 75
⇒ 11x = 105
x = 105 ÷ 11
Ratio high-quality : low-quality = 15 : (105 ÷ 11) = (15 × 11) : 105 = 165 : 105 = 11 : 7