GATE Mechanical 2019 Set 1 | GA | Question: 9

Question

A firm hires employees at five different skill levels P, Q, R, S, T. The shares of employment at these skills levels of total employment in $2010$ is given in the pie chart as shown. There were a total of $600$ employees in $2010$ and the total employment increased by $15\%$ from $2010$ to $2016$. The total employment at skill levels P, Q and R remained unchanged during this period. If the employment at skill level S increased by $40 \%$ from $2010$ to $2016$, how many employees were there at skill level T in $2016$?

• A. $30$
• B. $35$
• C. $60$
• D. $72$

Answer 1

Number of employees in $2010 = 600.$

Number of employees in $2016 = 1.15 \times 600 = 690.$

So, increase in $90$ employments is by $S$ and $T$ as other $3$ remained constant.

Original $S$ value $ = 0.25 \times 600 = 150.$

New $S$ value $ = 1.4 \times 150 = 210.$

So, increase in $S$ is $60$ and so increase in $T = 90-60=30.$

Original $T$ value $ = 0.05 \times 600 = 30.$

So, new $T$ value $ = 30 + 30 = 60.$

Correct Option: C.

Comments

Why in S 40% is taken as 1 + 0.4 = 1.4 rather than only 0.4 ? @Arjun Sir please answer.

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@ankit i think you are unaware of basics increase in 40 means increase in 100 so 100+40 =140 which in percentage writen as 1.4

Answer 2

$In\  2010: $

Total number of employees $ = 600$ 

Number of employees of skills $Q=R=S=25\%   \ \ of  \ \ 600 =\dfrac{25}{100}\times 600=150$

Number of employees of skill $P = 20\%  \ \ of \ \ 600 =\dfrac{20}{100}\times 600= 120$ 

Number of employees of skill $T= 5\%  \ \ of \ \  600 =\dfrac{5}{100}\times 600 =30$

$In \  2016:$ 

Total number of employees increased by $15\%$ Total number of employees $=1.15 \times 600 =690$ 

As there is no change in skill level of $P, Q, $ and $R$

Number of employees of skill level $P = 120$

Number of employees of skill level $Q = 150$ 

Number of employees of skill level $R=150$ 

Number of employees at skill level $S  \ 40\%$ increases $ = 1.4\times 150 = 210$

Number of employees at skill level $T  = 690-(120 +150+ 150 +210)= 60.$

So,the correct answer is $(C).$

Comments

Sorry SIr, it may sound silly but I am not able to understand how 40% is considered as 140%. Please elaborate.

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@ankit3009 let a quantity be 100 units when you increase it by 40% then the quantity will become 140 which is 1.4 times the original quantity which was 100 i,e (1.4 *100 = 140 ) which is 1 + 0,4 i.e 100 + 0,4*100 which will also give 140.

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@ankit3009

Suppose your height is 6 foot in year 2022.

And your height increases by 40% in year 2023.

Then what will you say about your new height:

Your new height=

40% of 6 foot 

= .40 * 6 = 2.4 foot 

no way , height increase means extra added in full previous height.

So,

new height = 

old height + percentage increase

i.e. your old height will be included 100% + 40 % increase in the height.

So new height = 100+40 % = 140% of your height of 2022. = 6 + 2.4 foot.

Answer 3

To solve this problem, we need to determine the number of employees at skill level T in 2016 based on the given information.

**Step 1: Calculate the number of employees at each skill level in 2010.**

The percentages and total number of employees (600) are given:

- Skill P: 20% of 600 = 0.20 × 600 = 120 employees
- Skill Q: 25% of 600 = 0.25 × 600 = 150 employees
- Skill R: 25% of 600 = 0.25 × 600 = 150 employees
- Skill S: 25% of 600 = 0.25 × 600 = 150 employees
- Skill T: 5% of 600 = 0.05 × 600 = 30 employees

**Step 2: Calculate the total number of employees in 2016.**

The total employment increased by 15% from 2010 to 2016:

- Total employees in 2016 = 600 × 1.15 = 690 employees

**Step 3: Determine the number of employees at each skill level in 2016.**

- Skills P, Q, R remained unchanged:
  - Skill P: 120 employees
  - Skill Q: 150 employees
  - Skill R: 150 employees
- Skill S increased by 40%:
  - Skill S in 2016 = 150 × 1.40 = 210 employees

**Step 4: Calculate the number of employees at skill level T in 2016.**

Subtract the total employees at skills P, Q, R, and S from the total employees in 2016:

- Total employees at P, Q, R, S = 120 + 150 + 150 + 210 = 630 employees
- Employees at skill T = Total employees in 2016 - Total employees at P, Q, R, S
- Employees at skill T = 690 - 630 = 60 employees

**Answer:**
60