Question

A basket of 2 apples, 4 oranges and 6 mangoes cost 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

• A. 12
• B. 13
• C. 11
• D. 10

Answer 1

Answer: (B)

13

Answer 2

Let's assume the cost of an apple is $a$, an orange is $o$, and a mango is $m$

From the given information:

1. For the first basket: $2a + 4o + 6m$

2. For the second basket: $a + 4o + 8m$

3. For the third basket: $8o + 7m$

Given that all the baskets cost the same, we can equate the cost expressions:

$2a + 4o + 6m = a + 4o + 8m$

From the above equation, $\left( a = 2m \right) ...(i)$

Similarly, from the second and third baskets:

$a + 4o + 8m = 8o + 7m$

Which gives, $\left( a + m = 4o \right) ...(ii)$

Substituting $a$ from equation (i) in equation (ii):

$( 2m + m = 4o ) ( 3m = 4o ) ( o = 0.75m ) ...(iii)$

Now, let's find the number of mangoes in a basket that costs the same as the other baskets, using only mangoes.

From the first basket:

$(2a + 4o + 6m ) = ( 2(2m) + 4(0.75m) + 6m)$

$= \left( 4m + 3m + 6m \right)$

$= ( 13m )$

So, a basket of 13 mangoes has the same cost as the other baskets.