The ratio of money with Ram and Gopal is 7 : 17, and the ratio of money with Gopal and Krishan is also 7 : 17. If Ram has Rs. 490, how much money does Krishan have?

Introduction / Context:
This problem involves chained ratios among three people Ram, Gopal and Krishan. The ratios relate Ram to Gopal and Gopal to Krishan, and the absolute amount with Ram is given. From this information, we are asked to determine the amount with Krishan. It tests the ability to work with linked ratios and to use a common variable approach effectively.

Given Data / Assumptions:

• The ratio of money with Ram and Gopal is 7 : 17.• The ratio of money with Gopal and Krishan is 7 : 17.• Ram has Rs. 490.• All amounts are positive and measured in rupees.• We are to find the amount of money with Krishan.

Concept / Approach:
We interpret the given ratios using variables. From Ram and Gopal's ratio, we write Ram's money as 7k and Gopal's as 17k. From Gopal and Krishan's ratio, we write Gopal's money as 7m and Krishan's as 17m. Since Gopal's actual money must be the same in both expressions, we equate 17k and 7m to establish a link between k and m. Once we know k from Ram's actual amount, we can compute m and then Krishan's amount. This method demonstrates how to handle multiple related ratio conditions.

Step-by-Step Solution:
Step 1: From the ratio Ram : Gopal = 7 : 17, let Ram have 7k and Gopal have 17k.Step 2: We are told that Ram has Rs. 490. So 7k = 490.Step 3: Solve for k: k = 490 / 7 = 70.Step 4: Therefore, Gopal has 17k = 17 * 70 = 1,190 rupees.Step 5: Now use the second ratio Gopal : Krishan = 7 : 17.Step 6: Let Gopal have 7m and Krishan have 17m according to this ratio.Step 7: Gopal's money must be the same in both descriptions, so 7m = 1,190.Step 8: Solve for m: m = 1,190 / 7 = 170.Step 9: Krishan's money = 17m = 17 * 170.Step 10: Multiply to find the product: 17 * 170 = 17 * (17 * 10) = 289 * 10 = 2,890.Step 11: Therefore, Krishan has Rs. 2,890.

Verification / Alternative check:
We can verify the consistency of ratios and amounts. Using k = 70, Ram has 490 and Gopal has 1,190. The ratio 490 : 1,190 simplifies by dividing both numbers by 70 to 7 : 17, which matches the first given ratio. Using m = 170, Gopal has 1,190 and Krishan has 2,890. The ratio 1,190 : 2,890 simplifies by dividing by 170 to 7 : 17, which matches the second given ratio. Since both ratios hold true with these amounts, our solution is consistent.

Why Other Options Are Wrong:
• Rs. 2,680: This would give a different ratio than 7 : 17 when compared with Gopal's 1,190.• Rs. 2,330: This would not maintain the ratio 7 : 17 with Gopal's amount and would contradict the given conditions.• Rs. 1,190: This is the amount with Gopal, not with Krishan, and it ignores the second ratio that requires Krishan to have more money.

Common Pitfalls:
Some students mistakenly assume that the same multiplier applies to all ratios simultaneously and try to use one variable instead of linking two sets of ratios through a shared quantity. Others may incorrectly assume that the ratio 7 : 17 applies directly between Ram and Krishan. Computational mistakes in handling large numbers or in simplifying ratios can also lead to errors. The crucial step is recognizing that Gopal is the common link and equating his two expressions to relate the different ratio multipliers.

Final Answer:
Krishan has Rs. 2,890.