Question:
Suppose,C1,C2,C3,C4, and C5 are five companies.The profits made by C1,C2, and C3 are in the ratio 9:10:8 while the profits made by C2,C4, and C5 are in the ratio 18:19:20.If C5 has made a profit of Rs19 crore more than C1,then the total profit (in Rs) made by all five companies is
Suppose,C1,C2,C3,C4, and C5 are five companies.The profits made by C1,C2, and C3 are in the ratio 9:10:8 while the profits made by C2,C4, and C5 are in the ratio 18:19:20.If C5 has made a profit of Rs19 crore more than C1,then the total profit (in Rs) made by all five companies is
Updated On: Jul 30, 2025
- 438 crore
- 435 crore
- 348 crore
- 345 crore
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The Correct Option is A
Solution and Explanation
Step 1: Define variables
Let the profits of C1, C2, C3, C4, and C5 be: \[ P_1, \ P_2, \ P_3, \ P_4, \ P_5 \]
Step 2: Ratio of P1, P2, P3
Given: \[ P_1 : P_2 : P_3 = 9 : 10 : 8 \] Let: \[ P_1 = 9x, \quad P_2 = 10x, \quad P_3 = 8x \]
Step 3: Ratio of P2, P4, P5
Given: \[ P_2 : P_4 : P_5 = 18 : 19 : 20 \] Let: \[ P_2 = 18y, \quad P_4 = 19y, \quad P_5 = 20y \]
Step 4: Relationship between x and y
Since \( P_2 = 10x = 18y \): \[ x = 1.8y \]
Step 5: Additional condition
Given: \[ P_5 = P_1 + 19 \] Substitute: \[ 20y = 9x + 19 \] Replace \( x \) with \( 1.8y \): \[ 20y = 9(1.8y) + 19 \] \[ 20y = 16.2y + 19 \] \[ 3.8y = 19 \] \[ y = 5 \]
Step 6: Find x
\[ x = 1.8y = 1.8 \times 5 = 9 \]
Step 7: Calculate profits
\[ P_1 = 9x = 81, \quad P_2 = 10x = 90, \quad P_3 = 8x = 72 \] \[ P_4 = 19y = 95, \quad P_5 = 20y = 100 \]
Step 8: Total profit
\[ \text{Total} = P_1 + P_2 + P_3 + P_4 + P_5 \] \[ = 81 + 90 + 72 + 95 + 100 = 438 \ \text{crore} \]
Final Answer:
\[ \boxed{\text{Total profit = 438 crore}} \]
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