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
Explanation:
Let the cost of each apple be ‘a’, each orange be ‘o’ and each mango be ‘m’.
∴ 2a + 4o + 6m = a + 4o + 8m = 8o + 7m
⇒ 2a + 4o + 6m = 8o + 7m ⇒ 4o + m = 2a …(1)
Also, a + 4o + 8m = 8o + 7m ⇒ 4o – m = a …(2)
Solving (1) and (2) we get 8o = 3a and m = a/2
∴ Value of each basked in terms of mangoes = 2a + 4o + 6m = 4m + 3a/2 + 6m = 10m + 3/2 × 2m = 10m + 3m = 13m
∴ Value of each basket is same as value of 13 mangoes.
Hence, option (a).
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