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CAT 2021 Quant Question [Slot 1] with Solution 09

Question
A basket of 2 apples, 4 oranges and 6 mangoes costs the same as a basket of 1 apple, 4 oranges and 8 mangoes, or a basket of 8 oranges and 7 mangoes. Then the number of mangoes in a basket of mangoes that has the same cost as the other baskets is
  1. 11
  2. 13
  3. 10
  4. 12
Option: 2
Solution:
Let the cost of an apple, an orange and a mango be a, o, and m respectively.
Then it is given that:
2a+4o+6m = a+4o+8m
or a = 2m.
Also, a+4o+8m = 8o + 7m
10m-7m = 4o
3m = 4o.
We can now express the cost of a basket in terms of mangoes only:
2a+4o+6m = 4m+3m+6m = 13m.
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