Multiple choice

There are three fruit sellers A, B and C. All of them have a mixture of two types of mangoes. A has (a + 6) kg of mangoes, B has 21 kg of mangoes less than A, while C has (a – 10) kg of mangoes. A, B and C have the two types of mangoes in the ratios 3 : 5, 7 : 8 and 9 : 7, respectively. If A sells 24 kg of mixed mangoes and adds 3 kg of the first type of mangoes, then the new ratio becomes 2 : 3 for him. If C adds x kg of the second type of mangoes to his mixture, then the new ratio of both types becomes 9 : 11 for him. What is the value of (a + x)?

  1. 50

  2. 60

  3. 110

  4. 90

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A = a+6, B = a+6-21 = a-15, C = a-10. A's ratio 3:5 means 3/8 of (a+6) is type 1. After selling 24kg (ratio 3:5, so 9kg type 1, 15kg type 2) and adding 3kg type 1, new ratio 2:3. (3/8(a+6) - 9 + 3) / (5/8(a+6) - 15) = 2/3. Solving for a: (3/8(a+6) - 6) / (5/8(a+6) - 15) = 2/3 => 9/8(a+6) - 18 = 10/8(a+6) - 30 => 1/8(a+6) = 12 => a+6 = 96 => a = 90. C has 80kg, ratio 9:7 (45kg type 1, 35kg type 2). Adding x kg type 2 gives ratio 9:11. 45 / (35+x) = 9/11 => 5 / (35+x) = 1/11 => 35+x = 55 => x = 20. a+x = 90+20 = 110.

AI explanation

From A's new ratio, the equation is 3a divided by 8 minus 14 plus 3 equals 2 times 7a divided by 8 minus 10 divided by 3. Solving this yields a equals 42. C's initial amount is 32 kg, containing 14 kg of the first type and 18 kg of the second type. Adding x kg to the second type gives 14 divided by 18 plus x equals 9 divided by 11, so x equals 68. The sum of a and x is 110.

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