CAT 2021 Slot 1 QA Question 21: 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

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

Accepted Answer

Let the costs of one apple, one orange and one mango be $a$, $o$ and $m$ respectively.
Comparing the first two baskets,
$2a + 4o + 6m = a + 4o + 8m$
$a = 2m$
Comparing the first and third baskets,
$2a + 4o + 6m = 8o + 7m$
$2a - 4o - m = 0$
Substitute $a = 2m$.
$4m - 4o - m = 0$
$o = \dfrac{3m}{4}$
N

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