## OGQR 2020: Question No. 376

A rectangular solid has length, width, and height of L cm, W cm, and H cm, respectively. If these dimensions are increased by x%, y%, and z%, respectively, what is the percentage increase in the total surface area of the solid?

- L, W, and H are in the ratios of 5:3:4.
- x = 5, y = 10, z = 20

Source | OG 2020 |

Type | Data Sufficiency |

Topic | Geometry/Word Problems |

Sub-Topic | Rectangular Solids/Percentages |

Difficulty | Hard |

## Solution

__Steps 1 & 2: Understand Question and Draw Inferences__

__Steps 1 & 2: Understand Question and Draw Inferences__

In this question, we are given

- A rectangular solid has length, width, and height of L cm, W cm, and H cm, respectively.

We need to determine

- The corresponding percentage increase in the total surface area of the solid, if the length, width, and height are increased by x%, y% and z% respectively.

The total surface area of the rectangular solid, before increase = 2(LW + LH + WH)

To increase the percentage of the total surface area, we need to know

- The values of L, W, H, before increase (or say, the ratio of L, W, H) and
- The values of x, y, and z.

With this understanding, let us now analyse the individual statements.

__Step 3: Analyse Statement 1__

__Step 3: Analyse Statement 1__

As per the information given in statement 1, L, W, and H are in the ratios of 5: 3: 4.

- However, from this statement, we cannot determine the values of x, y, and z.

Hence, statement 1 is not sufficient to answer the question.

__Step 4: Analyse Statement 2__

__Step 4: Analyse Statement 2__

As per the information given in statement 2, x = 5, y = 10, z = 20.

- However, from this statement, we cannot determine the values of L, W, and H (or their ratios).

Hence, statement 2 is not sufficient to answer the question.

__Step 5: Combine Both Statements Together (If Needed)__

__Step 5: Combine Both Statements Together (If Needed)__

Combining information from both statements, we get

- L: W: H = 5: 3: 4 and x = 5, y = 10, z = 20.

As we have all the necessary information to calculate the percentage increase, we can say the correct answer is option C.

### Takeaways

- Total Surface Area of a cuboid/rectangular box = 2(LW + WH + LH)
- If x is the original value and y is the increased value, then the percentage increase from x to y can be calculated as:
- Percentage increase = {(New – Original)/Original} * 100
- = {(y – x)/x} * 100

- Percentage increase = {(New – Original)/Original} * 100

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