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

The Correct Option is B

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.

Answer 2

Let the costs of an apple, an orange, and a mango be \( a \), \( o \), and \( m \) respectively. According to the question, we are given the following equations:

\[ 2a + 4o + 6m = a + 4o + 8m \] Simplifying: \[ 2a = 8m - 6m \] \[ a = 2m \]

Step 1: Solving the Second Equation

The second equation is: \[ a + 4o + 8m = 8o + 7m \] Simplifying: \[ 10m - 7m = 4o \] \[ 3m = 4o \] So we can express the cost of an orange as: \[ o = \frac{3}{4} m \]

Step 2: Expressing the Cost of a Basket in Terms of Mangoes

We need to express the cost of a basket, which is \( 2a + 4o + 6m \), solely in terms of mangoes: \[ 2a + 4o + 6m \] Substituting \( a = 2m \) and \( o = \frac{3}{4} m \): \[ = 4m + 3m + 6m \] \[ = 13m \]

Final Answer:

The cost of the basket is \( \boxed{13} \) mangoes.