2 biscuits and 1 chocolate cost ₹69. 2 chocolates and 3 cups of coffee cost ₹127. 3 biscuits, 4 chocolates and 2 cups of coffee cost ₹229. Find the total cost (in ₹) of 5 biscuits, 5 chocolates and 5 cups of coffee.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 355.
Let, the price of a biscuit, a chocolate, and a cup of coffee be ₹x, ₹y, and ₹z respectively.
So, 2x + y = 69 .....(1)
2y + 3z = 127 .....(2)
3x + 4y + 2z = 229 .....(3)
From equation (1), y = 69 - 2x .....(4)
Putting the value of y in equation (2),
2(69 - 2x) + 3z = 127
⇒ 138 - 4x + 3z = 127
⇒ -4x + 3z = -11
⇒ z = (-11 + 4x)/3 .....(5)
Putting the value of y and z in equation (3),
3x + 4(69 - 2x) + 2[(-11 + 4x)/3] = 229
⇒ 9x + 12(69 - 2x) + 2(-11 + 4x) = 687
⇒ 9x + 828 - 24x -22 + 8x = 687
⇒ 7x = 119
⇒ x = 119/7 = 17
Putting x = 17 in the equation (4) and (5),
y = 69 - 2(17) = 69 - 34 = 35
Also, z = (-11 + 4 × 17)/3 = 57/3 = 19
So, 5(x + y + z) = 5(17 + 35 + 19) = 5 × 71 = 355
Therefore, the total cost of 5 biscuits, 5 chocolates, and 5 cups of coffee is ₹355.