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.

Question

Accepted Answer

Let the cost of 1 biscuit = x, 1 chocolate = y, 1 cup of coffee = z.

We are given:
1) 2x + y = 69 ...(i)
2) 2y + 3z = 127 ...(ii)
3) 3x + 4y + 2z = 229 ...(iii)

We are to find: 5x + 5y + 5z = 5(x + y + z)
So, first, let's solve for x, y, z.

Step 1: From (i): 2x + y = 69 => y = 69 - 2x

Step 2: Substitute y into (iii):
3x + 4y + 2z = 229
=> 3x + 4(69 - 2x) + 2z = 229
=> 3x + 276 - 8x + 2z = 229
=> -5x + 2z = 229 - 276
=> -5x + 2z = -47
=> 5x - 2z = 47 ...(iv)

Step 3: From (ii): 2y + 3z = 127
Substitute y = 69 - 2x:
2(69 - 2x) + 3z = 127
=> 138 - 4x + 3z = 127
=> -4x + 3z = 127 - 138
=> -4x + 3z = -11
=> 4x - 3z = 11 ...(v)

Now, solve equations (iv) and (v):
(iv)  5x - 2z = 47
(v)   4x - 3z = 11

Multiply (iv) by 3: 15x - 6z = 141
Multiply (v) by 2: 8x - 6z = 22
Subtract:
(15x - 6z) - (8x - 6z) = 141 - 22
=> 7x = 119
=> x = 17

Now, substitute x = 17 into (iv):
5x - 2z = 47
5*17 - 2z = 47
85 - 2z = 47
-2z = 47 - 85 = -38
2z = 38
z = 19

Now, y = 69 - 2x = 69 - 34 = 35

So, x = 17, y = 35, z = 19

Now, 5x + 5y + 5z = 5(x + y + z) = 5*(17 + 35 + 19) = 5*71 = 355

But this is not matching with the options marked as correct. Let's check calculations:

x = 17, y = 35, z = 19
Check in (ii): 2y + 3z = 2*35 + 3*19 = 70 + 57 = 127 (correct)
Check in (iii): 3x + 4y + 2z = 3*17 + 4*35 + 2*19 = 51 + 140 + 38 = 229 (correct)

So, 5x + 5y + 5z = 5*71 = 355

But the options are: 304, 375, 345, 355

So, the correct answer is 355.

Therefore, Option 4 is correct.

Answer

Answer

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