Linda, Robert, and Pat packed a certain number of boxes with books. Wh

I) \(\frac{3(P+R+L)}{10}=L\)

II) \(R=P+10\)

II) in I): \(\frac{3(2P+10+L)}{10} =L\implies 6P+30=7L\)

II) in I) \(\frac{3(R+R-10+L)}{10}=L \implies 6R-30=7L\)

We cannot use \(L\) to compare \(R\) and \(P\). E

Step 1: Analyse Question Stem

Let the number of books packed by Linda, Robert and Pat be L, R and P respectively.
The ratio of R : P has to be found out.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1: Linda packed 30 percent of the total number of boxes of books.

If the total number of books packed by the three is 100, then we can only say that L = 30 and R + P = 70.

However, we cannot find out the exact values of R and P and hence cannot find the value of the ratio of R:P

The data in statement 1 is insufficient to find a unique value of the required ratio.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.

Statement 2: Robert packed 10 more boxes of books than Pat did.

This means R = P + 10; therefore, the required ratio = \(\frac{P + 10 }{ P}\)

Statement 2 does not give us the value of P, hence the exact value of the ratio cannot be calculated.

The data in statement 2 is insufficient to find a unique value of the required ratio.
Statement 2 alone is insufficient. Answer option B can be eliminated.

Step 3: Analyse Statements by combining

From statement 1: Linda packed 30 percent of the total number of boxes of books.
From statement 2: Robert packed 10 more boxes of books than Pat did.

If the total number of books = 100, then L = 30, R + P = 70 and R = P + 10.
Solving for R and P, we get, R = 40 and P = 30. R : P = 4 : 3

If the total number of books = 200, then L = 60, R + P = 140 and R = P + 10.
Solving for R and P, we get, R = 75 and P = 65. R : P = 15 : 13

Combining the statements is not sufficient to give us a unique value for the required ratio.

The combination of statements is issufficient to find a unique value of the required ratio.
Statements 1 and 2 together are insufficient. Answer option C can be eliminated.

The correct answer option is E.

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