The weight of C is twice the weight of M. The weight of M is one ninth of the weight of R. The weight of R is five by two times the weight of K. The weight of K is one third of the weight of G. Who is the second lightest among C, M, K, G and R?

Introduction / Context:
This problem compares the weights of five people or objects, named C, M, K, G and R, using a chain of proportional relationships. You are not given explicit weights in kilograms, but instead how each weight relates to another. The task is to find who is the second lightest, which requires building an ordering from lightest to heaviest based on these ratios. It is a good exercise in translating fractional relationships into a consistent ranking.

Given Data / Assumptions:

• C is twice as heavy as M.
• M is one ninth of the weight of R.
• R is five by two times the weight of K.
• K is one third of the weight of G.
• All weights are positive and distinct.
• We want to identify the second lightest among C, M, K, G and R.

Concept / Approach:
A clear strategy is to express all weights in terms of a single base variable, such as M. Once each person weight is written as a multiple of M, it is straightforward to compare them numerically. Because multipliers are all positive, the order of the coefficients directly reflects the order of the actual weights. We can then sort these coefficients from smallest to largest to find the lightest and second lightest individuals.

Step-by-Step Solution:
Step 1: Let the weight of M be M units. We will express all other weights in terms of M.Step 2: From “C is twice the weight of M”, we get C = 2M.Step 3: From “M is one ninth of the weight of R”, we have M = R / 9, so R = 9M.Step 4: From “R is five by two times the weight of K”, we have R = (5 / 2) * K. Substituting R = 9M gives 9M = (5 / 2) * K.Step 5: Solve this for K: K = (2 / 5) * 9M = (18 / 5) * M, which is 3.6M.Step 6: From “K is one third of the weight of G”, we have K = G / 3, so G = 3K.Step 7: Substitute K = (18 / 5) * M into G = 3K to get G = 3 * (18 / 5) * M = (54 / 5) * M, which is 10.8M.Step 8: Now list all weights in terms of M: M = 1M, C = 2M, K = 3.6M, R = 9M, G = 10.8M.Step 9: Order these coefficients from smallest to largest: 1, 2, 3.6, 9 and 10.8, corresponding to M, C, K, R and G respectively.Step 10: The lightest is M and the second lightest is C.

Verification / Alternative check:
You can assign a concrete value to M, for example M = 10 kilograms, and compute all weights explicitly. Then C = 20, K = 36, R = 90 and G = 108 kilograms. Clearly the order from lightest to heaviest is M (10), C (20), K (36), R (90), G (108). The second lightest remains C. Any positive choice for M will preserve the ordering because all relations are linear and proportional.

Why Other Options Are Wrong:
M is the lightest, not the second lightest, since all other weights are multiples greater than 1 times M. K is heavier than both M and C because 3.6M is greater than 2M. R and G are much heavier, being 9M and 10.8M, so they are nowhere near the bottom end of the ranking. Therefore options b, c and d cannot represent the second lightest individual.

Common Pitfalls:
Some learners confuse phrases like “one ninth of” and “five by two times” and invert the fractions incorrectly. Another common error is trying to reason purely in words without expressing the relationships algebraically, which can lead to inconsistent or mistaken comparisons. Writing each expression in terms of one base weight and then comparing numerical coefficients is the safest approach.

Final Answer:
The second lightest among the five is C.