Question

3 mangoes and 4 apples costs Rs 85. 5 apples and 6 peaches costs Rs. 122. 6 mangoes and 2 peaches cost Rs.114. what is the combined price of 1 apple, 1 peach and 1 mango?
option
(a) 37 Rs
(b) 39 Rs
(c) 35 Rs
(d) 36 Rs; 3 mangoes and 4 apples costs Rs 85. 5 apples and 6 peaches costs Rs. 122. 6 mangoes and 2 peaches cost Rs.114. what is the combined price of 1 apple, 1 peach and 1 mango?; option; (a) 37 Rs; (b) 39 Rs; (c) 35 Rs; (d) 36 Rs

Answer 1

Here, Apple = 10

Mango=15

Peache=12

Answer 2

Answer:  The correct option is (a) Rs. 37.

Step-by-step explanation:  Given that the cost of 3 mangoes and 4 apples is Rs 85, the cost of 5 apples and 6 peaches is Rs. 122 and the cost of 6 mangoes and 2 peaches is Rs.114.

We are to find the combined cost of 1 apple, 1 peach and 1 mango.

Let Rs, x, Rs, y and Rs. z represents the respective prices of 1 apple, 1 peach and 1 mango.

Then, according to the given information, we have

$4x+3z=85~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\5x+6y=122~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\2y+6z=114~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Multiplying equation (iii) by 3, we have

$3(2y+6z)=3\times114\\\\\Rightarrow 6y+18z=342~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)$

Subtracting equation (ii) from equation (iii), we get

$(6y+18z)-(5x+6y)=342-122\\\\\Rightarrow 18z-5x=220\\\\\Rightarrow z=\dfrac{220+5x}{18}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(v)$

Substituting the value of z from equation (v) in equation (i), we get

$4x+3\times\dfrac{220+5x}{18}=85\\\\\\\Rightarrow \dfrac{72x+660+15x}{18}=85\\\\\Rightarrow 87x+660=1530\\\\\Rightarrow 87x=870\\\\\Rightarrow x=\dfrac{870}{87}\\\\\Rightarrow x=10.$

From equation (v), we get

$z\\\\\\=\dfrac{220+5\times10}{18}\\\\\\=\dfrac{220+50}{18}\\\\\\=\dfrac{270}{18}\\\\=15.$

From equation (ii), we get

$5\times10+6y=122\\\\\Rightarrow 6y=122-50\\\\\Rightarrow 6y=72\\\\\Rightarrow y=\dfrac{72}{6}\\\\\Rightarrow y=12.$

So, the price of 1 apple = Rs. 10,

the price of 1 peach = Rs. 12

and

the price of 1 mango = Rs. 15.

Therefore, the combined price of 1 apple, 1 peach and 1 mango is

$A=x+y+z=10+12+15=37.$

Thus, the combined price of 1 apple, 1 peach and 1 mango is Rs. 37.

Option (a) is CORRECT.