Multiple choice

The ratio of prices of onion last year and this year is $5 : 6$. The ratio of prices of potato last year and this year is $7 : 8$. The sum of prices of a kg of onion and potato this year is $48$ Rs. Find the price of onion (in Rs) last year if it was $\displaystyle \left ( \frac{20}{21} \right )$ of the price of potato last year?

  1. $15$
  2. $20$
  3. $25$
  4. $30$
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B Correct answer
Explanation

Onion: Last year = 5x, This year = 6x. Potato: Last year = 7y, This year = 8y. 6x + 8y = 48. Onion last year (5x) = (20/21) * Potato last year (7y) = (20/21) * 7y = (20/3)y. So 5x = 20y/3, x = 4y/3. Substitute: 6(4y/3) + 8y = 48. 8y + 8y = 48. 16y = 48, y = 3. x = 4(3)/3 = 4. Onion last year = 5x = 5(4) = 20.

AI explanation

Let last year's prices of onion and potato be O and P; we are given O = (20/21)P, which means the ratio O : P is 20 : 21. Let O = 20x and P = 21x; this year's prices become (6/5) of 20x for onion, which is 24x, and (8/7) of 21x for potato, which is 24x. The sum of this year's prices is 24x + 24x = 48x, which equals Rs. 48, so x equals 1. Last year's price of onion was 20x, which is Rs. 20.

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