GATE ECE 2021 | GA | Question: 9

Question

 

The number of minutes spent by two students, $X$ and $Y$, exercising every day in a given week are shown in the bar chart above.

The number of days in the given week in which one of the students spent a minimum of $10\%$ more than the other student, on a given day, is

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Answer 1

We can calculate the number of days in the given week in which one of the students spent more time than the other.

If $X$ is more than $10\%$ of $Y$ then $Y$ should be minimum and vice-versa.

• On Monday, the required percentage $ = \left(\dfrac{70-45}{45}\right) \times 100\% = 55.55\%$
• On Tuesday, the required percentage $ = \left(\dfrac{65-55}{55}\right) \times 100\% = 18.18\%$
• On Wednesday, the required percentage $ = \left(\dfrac{60-50}{50}\right) \times 100\% = 20\%$
• On Thursday, the required percentage $ = \left(\dfrac{60-55}{55}\right) \times 100\% =  9.09%$
• On Friday, the required percentage $ = \left(\dfrac{35-20}{20}\right) \times 100\% =  75\%$
• On Saturday, the required percentage $ = \left(\dfrac{60-50}{50}\right) \times 100\% = 20\%$
• On Sunday, the required percentage $ = \left(\dfrac{65-55}{55}\right) \times 100\% = 18.18\%$

$\therefore$ Total $6$ days are there, when one of the students spent a minimum of $10\%$ more than the other student.

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

Comments

Faster one :
On everyday check whether the 1.1 times of smaller value is <= the larger value. If yes then the day counts.
Suppose on Saturday : (1.1)*55 = 60.5 <= 65

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Faster approach:

• Spot the difference between both bars(easily viewable from the graph)
• Take 1/10th of the smaller bar
  • if 1/10th of the bar is equal or smaller than the difference => condition satisfied
  • else condition not satisfied

 

Answer 2

I saw the answers here and suprised , how long approach people are telling .These Approach sure your marks But they doesn't give you good ranks .

by method by just seeing the graph : on every day there are two representation ,so see the less one .

on sunday it's 55 so calculate 10 % of 55 in mind it would be roughly around 5.5.And now see is the bigger no is more than smaller no on sunday + 5.5 if yes then increase count =1;

and observe most of the smaller no on each day the weeks is 55,50,45 so you don't need to calculate % by applying formula .Make it simple and save time.

simlarly do it for other days also you don't need to use pen for this question .

I personally solved it in 30 sec ,even if you a little slow you can eaily solve in 1 minute.

Answer is 6.

Comments

did it same way!

 

Answer 3

Answer: C

 

On Sunday 10% *55= 5.5  Now 65 >=55+5.5   True

On Saturday 10%*50=5  Now 60>=55+5 True

On Friday 10%*20=2 Now 35>=20+2 True

On Thursday 10%*55=5.5 Now 60 >= 55+5.5 False

On Wednesday 10%*50=5 Now 60>= 50+5 True

On Tuesday 10%*55=5.5 Now 65>=55+5.5 True

On Monday 10%*45=4.5 Now 75>=45+4.5 True

Total 6 Days are True

Hence C is the Answer