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.
355
Let the cost of:
- 1 biscuit = \( B \)
- 1 chocolate = \( C \)
- 1 cup of coffee = \( K \)
From the given equations:
1. \( 2B + C = 69 \)
2. \( 2C + 3K = 127 \)
3. \( 3B + 4C + 2K = 229 \)
Step 1: Solve for \( C \) from Equation 1:
\( C = 69 - 2B \)
Step 2: Substitute \( C \) in Equation 2:
\( 2(69 - 2B) + 3K = 127 \)
\( 138 - 4B + 3K = 127 \)
\( 3K = 4B - 11 \) → \( K = \frac{4B - 11}{3} \)
Step 3: Substitute \( C \) and \( K \) in Equation 3:
\( 3B + 4(69 - 2B) + 2(\frac{4B - 11}{3}) = 229 \)
\( 3B + 276 - 8B + \frac{8B - 22}{3} = 229 \)
Multiplying by 3 to clear fractions:
\( 9B + 828 - 24B + 8B - 22 = 687 \)
\( -7B + 806 = 687 \)
\( 7B = 119 \) → \( B = 17 \)
Step 4: Find \( C \) and \( K \):
\( C = 69 - 2(17) = 35 \)
\( K = \frac{4(17) - 11}{3} = \frac{68 - 11}{3} = \frac{57}{3} = 19 \)
Step 5: Find total cost for 5 biscuits, 5 chocolates, and 5 cups of coffee:
\( 5B + 5C + 5K = 5(17) + 5(35) + 5(19) \)
\( = 85 + 175 + 95 \)
\( = 355 \)
Thus, the correct answer is option 1.
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