A’s money is to B’s money as 4 : 5, and B’s money is to C’s money as 2 : 3. If A has Rs. 800, how much money does C have?

Introduction / Context:
This problem composes two ratios to derive a three-term ratio A : B : C. Using A’s actual amount, we scale the ratio to find C’s amount.

Given Data / Assumptions:

• A : B = 4 : 5.
• B : C = 2 : 3.
• A has Rs. 800; find C.

Concept / Approach:
Equalize the middle term (B) across both ratios and combine to get A : B : C. Then use A’s actual value to determine the scale factor and compute C.

Step-by-Step Solution:
Make B common: A : B = 4 : 5 ⇒ multiply by 2 ⇒ 8 : 10. B : C = 2 : 3 ⇒ multiply by 5 ⇒ 10 : 15. Thus A : B : C = 8 : 10 : 15. If A = 8 parts = Rs. 800 ⇒ 1 part = Rs. 100. C = 15 parts = 15 * 100 = Rs. 1500.

Verification / Alternative check:
B = 10 parts = Rs. 1000 satisfies both given ratios with A = 800 and C = 1500.

Why Other Options Are Wrong:
Rs. 1000 and Rs. 1200 mis-scale the ratio; Rs. 2000 overstates C’s share.

Common Pitfalls:
Adding ratios instead of forming a compound ratio, or not equalizing the B terms before combining. Always align the shared term correctly.

Final Answer:
Rs. 1500