Aptitude - Average - Discussion

1. 

In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?

[A]. 6.25
[B]. 6.5
[C]. 6.75
[D]. 7

Answer: Option A

Explanation:

Required run rate = 282 - (3.2 x 10) = 250    = 6.25
40 40

Video Explanation: https://youtu.be/GhK9d8tcqvA


Vinod said: (Jul 16, 2010)  
Why we are writing 3.2*10 ?

Dilepkumar said: (Jul 20, 2010)  
They asking only remainig 40 over run rate. So why use of first 10 over?

Kavita said: (Jul 21, 2010)  
How do we arrive at the solution.? What is the logic?

Pratik Mehta said: (Jul 22, 2010)  
@Kavita : Run rate * overs = runs scored.

So now Run rate = Runs scored/required / overs.

There 282 - (3.2 x 10) = Runs required

Remaining overs are 40.

Ranjith said: (Aug 17, 2010)  
Why do we minus 282-(3.2*10)...?

Muhundhan said: (Aug 18, 2010)  
So we calculate the runs in the first 10 overs
first 10 overs they got 32 runs
remaining 40 overs they got 250
250 / 40 =6.25

Abc said: (Sep 10, 2010)  
Thanks muhundhan thats great.

Swetha said: (Dec 2, 2010)  
Why are you minus that 282 runs?

Tarun said: (Dec 13, 2010)  
282 are not minus,here ((3.2(current run rate)*10(overs))=32runs)
are subtracted from total required runs,so 282-32=250 are the runs required in other 40 overs,
so required run rate=
250/40=6.25 runs per over.

Avinsh said: (Dec 28, 2010)  
How to solve given problem:.

Rajana traveled a journey of 500km with speed of 50km/hr for 5 liter and traveled withe speed of 60km/hr for 5hr and then is last 5hr covers a distance of 700km and after taking rest of 3 hr again traveled. For 2 hr by covering a distance 120km find average of speed.

Nikhil said: (Jan 6, 2011)  
Why you write 283- (3. 2*10)?

Deepa said: (Jan 13, 2011)  
@nikhil

First we have to find no of runs scored in first 10 overs, to calculate runs scored in 10 overs we have to do 3.2*10 (means runsscored=runrate*no of overs).we get 32runs which means they have scored 32 runs in first 10 overs. so 283-32=250 runs should be scored in next 40 overs.to find the runrate, runrate=250/40 (we have to divide no of required runs by no of overs left)

Swathy said: (Jan 20, 2011)  
Excellent deepa and muhunthan.

Srinivas Reddy said: (Feb 3, 2011)  
First we calculate the total runs done in 10 overs by using run rate ie 10*3.2 (runs per over) = 32.

Remaining runs is 283-32 = 250.

The run rate required to achieve the target is 250 (required runs to do) /40 (remaining overs).

Gdged said: (Feb 15, 2011)  
Why we are using this formula?

Vinoth M said: (Feb 17, 2011)  
Formula is, average=sum of runs in each overs(s)/number of overs(n)
given n=10,average=3.2
Then,substitute values in formula,
->3.2=s/10
->s=32
in 10 overs total run is 32
target=282
Then in 40 overs thy need 250 runs
here n=40,s=250
percentage=s/n=250/40=6.25
So ans=6.25

Kalaivani said: (Apr 25, 2011)  
Why you write 283- (3. 2*10)?

Sathi said: (Jul 1, 2011)  
@kalaivani,

We want to calculate how many runs needed for remaining 40 overs to find the run rate for remaining overs.

283 is total score req for 40 overs,10*3.2=32 runs scored in the first over

Nayan Das said: (Jul 2, 2011)  
Very good explanation vinoth m, thanks.

Tanvir said: (Jul 16, 2011)  
It may be like this:
Let the required run rate be x.

Then Run in 40 overs = 40x (Becoz run rate = run per over)
Run in 10 overs= 10x3.2 (It is given that run rate of 10 overs is 3.2)
We know we required to calculate the run rate for 282 runs.

Then according to question:
3.2x10+40x=282
32+40x=282
40x=250
x=250/40=6.25 ans

Isha Panchal said: (Aug 20, 2011)  
Muhundhan sir thanks.

Nithinvino said: (Sep 5, 2011)  
Thanks muhundan.

Tintu Mathew said: (Sep 14, 2011)  
The simple method is

total runs takes in 10 over=3.2*10=32
we know dat target is 282
so
32+40*x=282
from this we get required run rate.

Aymen said: (Sep 27, 2011)  
Muhundan you are really very helpful.

How should I solve this.

The average of three numbers is 8, that of the first two is 11. Find the third number?plz help me.

Gautam said: (Sep 27, 2011)  
THE AVERAGE OF THREE NO.IS
X+Y+Z/3=8
THE SUM OF FIRST TWO NO. IS 11,SO
(X+Y)+Z/3=8
11+Z/3=8
BY TRANSPOSITION
11+Z=3*8
11+Z=24
Z=24-11
Z=13
Z

Arti said: (Oct 3, 2011)  
Thanks muhundhan thats great.

Radhika said: (Nov 3, 2011)  
Is there any formula?

Jay said: (Nov 25, 2011)  
Thank you very much muhundhan. Simple answer to understand.

Dkb said: (Jan 4, 2012)  
Pratik and Muhundhan Thanks for simplifying the problem.

Maha said: (Jan 17, 2012)  
Thanks vignesh mahesh.

Naresh said: (Mar 2, 2012)  
Hi friends, please think logically.

(1) Run rate of 10 ovres is 3.2 (i.e 3.2*10=32runs).

(2) Total runs are 282(i.e 282-32=250)

(3) Now check given answers....take 6.2runrate and 40 overs(i.e 6.25*40=250). So ans is "6.25" .

Ravi said: (Mar 15, 2012)  
We need to calculate remaining average so we have to deduct score whick is already scored.

Ashish said: (Mar 25, 2012)  
Hi friends, please think logically.

(1) Run rate of 10 ovres is 3.2 (i.e 3.2*10=32runs).

(2) Total runs are 282(i.e 282-32=250

(3) In 40 overs runs are 250.

Now, Run rate is 250/40 = 6.25 //

Gangaraju T C said: (Apr 22, 2012)  
First 10 overs Score = 10 overs x 3.2 Run Rate = 32 Runs.
Total targeted runs in 50 overs = 282 Runs
Required Runs to be scored in 40 overs = 250
Total 50 overs Runs(282 Runs)-First 10 overs runs Scored(32 Runs)
Required Run Rate in 40 overs = Required Runs/Remaining overs
= 250 Runs /40 overs
= 6.25

Soudri said: (Apr 24, 2012)  
10*3.2=32
So 282 - 32 = 250/40= 6.25

Colbie said: (May 6, 2012)  
Mr.A average on 4 test is 80. what does he need on his fifth test to raise his average to 84?

Apple said: (Jul 20, 2012)  
@Colbie.

Use this formula to solve the problem:

Average = sum of runs/number of tests.

Given that, average on 4 tests is 80.

Hence, Sum of runs scored = 80 x 4 = 360.

To calculate the number of runs he needs in his fifth test to raise his average to 84 is,

84 = 360 + x / 5 (use the formula given above).

x = 420 - 360 = 60 (answer).

Banita said: (Aug 21, 2012)  
Excellent explanation Tarun and Deepa, Thanks a lot

Sushank said: (Dec 10, 2012)  
Run rate in first ten overs = 3.2
Total runs made in first ten overs = 3.2*10 = 32 runs
Remaining runs to make = 282-32 =250
Overs left = 40 overs
Average run rate = 250/40 = 6.25

So, The run rate to make 250 runs in 40 overs is 6.25 RPO(runs per over)

Pradeep said: (Feb 15, 2013)  
Total run in 10 over=10*3.2=32
Required run in 40 over=282-32=250
Hence avg=250/40 =6.25

Ramya said: (Jun 23, 2013)  
What is the actual formula for this type of questions?

Vinod Anand said: (Aug 28, 2013)  
In the first 10 overs the run rate was = 3.2.

Than total run is = 32.

Where total target is - 282.

Let the remaining 40 overs run rate is = x.

32+40x = 282.

40x = 250.

x = 25/4 = 6.25 answer.

Amit said: (Dec 27, 2013)  
Using basics of cricket.

Runs in 10 overs at the rate of 3.2 = 32.

Target 282.

Remaining runs 282-32 = 250.

Remaining overs 40.

Thus run rate 250/40 = 6.25.

Akshata said: (May 25, 2014)  
Formula used for this type of questions?

Deebika.C said: (Jun 6, 2014)  
What is the formula for this sum?

Aayush said: (Jun 14, 2014)  
@Gautam - Sorry to say but your solution is wrong.
@Aymen - The solution for your problem stated.

"The average of three numbers is 8, that of the first two is 11. Find the third number?please help me." is:

Let three numbers be x,y,z.
Average of first three numbers is 8.
Hence, x+y+z/3 = 8.
=> x+y+z = 24.....eq(1).

Average of first two numbers is = 11.
Hence, x+y/2 = 11.
=> x+y = 22....eq(2).

Now substitute eq(2) value in eq(1).
Thus, 22+z = 24.
=> z = 24-22 = 2.
Answer is z = 2.
:).

Mudassir Pasha said: (Jun 19, 2014)  
The total target for 50 overs is 282 out of that first 10 overs they scored at The run rate of 3.2, which means they scored 32,
For remaining 40 overs the target is 282-32=250,

For 40 overs the target is 250.

Then for 1 over it is 250/40 = 6.25.

Palani said: (Jul 4, 2014)  
@Aayush - Sorry to say but your solution is wrong.
@Aymen - The solution for your problem stated.

THE AVERAGE OF THREE NO.IS
X+Y+Z/3=8.

THE SUM OF FIRST TWO NO. IS 11,SO
(X+Y)+Z/3=8.
11+Z/3=8.

BY TRANSPOSITION,
11+Z=3*8.
11+Z=24.
Z=24-11.
Z=13.

i.e) X+Y=11.
Z=13.

HENCE THE AVG X+Y+Z/3=8.

SO, Gautam IS RIGHT YOU'RE WRONG Ayush.

Manish said: (Sep 11, 2014)  
Why we Divided 40 over because remaining over 30 and you also given the 10 over run ate?

Dhananjay Gahmari said: (Nov 1, 2014)  
Sorry @Palani your point of view to check answer is wrong!

GAUTAM AND AYUSH you BOTH are RIGHT.

Gautam takes the sum of first two number is 11, and Ayush takes the average first two number is 11.

So both answer is correct.

Sudhir Joshi said: (Nov 27, 2014)  
In 10 overs run scored is 250, and in remaining 40 overs to get the total target of 282, remaining runs are 250 as 32 has been scored. Divide 250 by 40 that will be the required run-rate.

Raj said: (Jan 12, 2015)  
10*3.2 = 32.
40*? = ?
Required = 282.

Rashmi said: (Feb 24, 2015)  
Is there any short cut for this?

If we solve this way like long method, rest of the questions will be pending. Any one suggest me?

Hemanth said: (Feb 25, 2015)  
First 10 overs they scored 32 runs====3.2*10.

Then we required to score 250 runs to get the score of 282 in 40 overs=======(28232 = 250 in 40 overs).

Therefore: 250/40 = 6.25.

Rituparna Sengupta said: (Apr 3, 2015)  
Required run-rate = (282-(3.2*10))/40 = 6.25.

Rituparna Sengupta said: (Apr 3, 2015)  
(282-(3.2*10))/40 = 6.25.

Ako Venuh said: (Apr 14, 2015)  
We Know Run Rate = Runs/overs.

Therefore, in the first 10 overs.

Run Rate = Runs/Overs.
3.2 = Runs/10.

Runs = 3.2*10.
Runs = 32.

Now 32 runs is scored in the first 10 Overs.

Target = 282.
Target = 282-32 = 250.

Run Rate = Target runs/Remaining Overs.
Run Rate = 250/40.

Run Rate = 6.25.

Vasavi said: (Jul 12, 2015)  
@Apple.

You give example test match in that problem 80*4 = 320 but you tack it as 360?

Padmashri said: (Jul 14, 2015)  
RR runs Target-282.

1-10 overs 3.2 32.

11-40 overs ? 250.

RR = Runs/Overs.

RR = 250/40.

Answer: 6.25.

Swetha said: (Aug 6, 2015)  
Iron manufacturing company produced a total of 3000 tons of iron in January of a particular year. Starting from February its production increased by 200 tons every month over the previous months until the end of that year. Find its average monthly production (in tons) for that year.

Sameer Rolekar said: (Aug 11, 2015)  
Note we have a formula => Runrate*Overs = Run Scored.

1st > we have given Runrate and overs, so we are calculating the run scored.

ie. 3.2*10 = ? (Run Scored) we get Run scored = 32.

2nd > we have to find the run scored in the remaining 40 overs so we subtract the run scored in the first 10 over from the Total score.

i.e. 282-32=250.

Now we have run scored=250 and overs=40, so we find will find the run rate.

i.e. Runrate*Overs = Run Scored.

Runrate*40 = 250.

Answer==> Runrate = 6.25.

Santhosh said: (Sep 1, 2015)  
First we calculate 10 overs score using run rate (3.2).

= 10*3.2 = 32 runs.

Target = 282.

We need 250 runs in 40 overs (282-32).

So, 250/40 = 6.25.

Akila said: (Nov 30, 2015)  
Let the run in 5th match be x.

Total runs scored in 4 matches = 80*4 = 320.

Now, when 320 added with x avg becomes 84 (as per question).

= (320+x)/5 = 84.

x = 100.

Answer check: (320+100)/5 = 84.

Jitender said: (Dec 4, 2015)  
Ten over run rate is 3.2

So 10*3.2= 32.

Then Target 282-32 = 250.

Remaining over is 40.

250/40= 6.25 answer.

Shobhita said: (Jan 5, 2016)  
Why we are minus 282 - 32?

Manish said: (Feb 14, 2016)  
I need basic method.

Manish said: (Feb 25, 2016)  
@Ms. Shobhita.

1 over for 6 balls should be getting 1run for every ball is 6 runs for 6 balls. 1 over 6run rate. 10 overs 32 runs. Run rate was 3.25.

32 runs subtracted for target run 282. Remain 250. Balance 40 overs. Every ball get one run reach in 240. Answer is 6.25.

Swarna said: (Mar 8, 2016)  
What is the formula of this?

Kasturee Bhattacharyya said: (Mar 8, 2016)  
It's simple.

He scored 32 runs in 10 overs (Run rate (3.2)* Over (10)=32).

Remaining Score 282-32 = 250 Runs.

Again, Run Rate* Over = Score.

Run Rate = Score/ Over.
= 250/40
= 6.25

Naga Venkatesh said: (May 6, 2016)  
We know run rate = average.

Sum of scores in 10 overs/10 = 3.2 => sum = 32.

Sum of scores in 40 overs / 40 = ?

Already we got 32 runs in 10 overs so we have to get 250 runs.

From options 40*6.25 = 250, So it should be the answer.

Sanjay Gurjar said: (Jun 19, 2016)  
282 - 32/40 = 6.25.

Pranav said: (Jun 29, 2016)  
Can anyone please give the solution of this.

A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th innings.

Sonu Kumar Sharma said: (Jul 22, 2016)  
You all explained very well thanks.

Hareesh said: (Aug 1, 2016)  
For this problem no need of any formula just we need only mind calculation first 10 overs 3.2 run rate means they scored 32 runs our target is 282. So we have to deduct 32 from 282 remaining is 250 we need to calculate for 40 overs.

So for 240 balls we need 250 runs so divide 250 by 40 overs we get 6.25.

Pallavi Mansingh said: (Aug 15, 2016)  
Thanks @Hareesh.

Vinay said: (Aug 29, 2016)  
@Dilepkumar.

The game is of 50 overs is directly said.

Amit Soni said: (Sep 18, 2016)  
Its real solution is that,

282 = 5.64 * 50 = 40 * req run rate + 3.2 * 10 then answer is 6.25 means.

Total scored run in 50 over = total run rate * over = 40over * run rate + 10over * run rate.

Poulami said: (Sep 20, 2016)  
@Tanvir, you are superb.

Suman said: (Sep 22, 2016)  
Run = (no of runs took in one over)/(total possible no of runs),

So, instead of 3.2 = x/10, it should be 3.2 = x/(10 * 6),

Since, 1 over has 6 runs?

Mike said: (Sep 23, 2016)  
The average monthly expenditure of Ravi was 100 during the first 3 months. 2200 during the next 4 months and 4620 during the subsequent five months of the year. If the total saving during the year was 2100. Find Ravi's average monthly income.

Ramesh Kanna said: (Sep 28, 2016)  
@Mike.

avg = sum of observations/number of observatios.
Avg expenditure = 100.
Number of months = 3.
So, sum = 100 * 3 = 300.

Similarly for rest of the months 8800 and 23100 respectively.
Total income = expenditures + savings.
So, 300 + 8800 + 23100 + 2100 = 34300.
Avg income = total income/12(months).
Avg = 34300/12 = 2858.

Manoj said: (Sep 30, 2016)  
You have 2 candles each burn for 1 hour tell when the time is 45 minutes.

Rajaram said: (Oct 20, 2016)  
O A R
10 3.2 32
40 x 250 (282-32).

x = 250/40 = 6.25.

Nish said: (Oct 24, 2016)  
Over * run rate = run => 10 * 3.2 = 32 runs.

Target = 282, our score is 32 runs so required run => 282 - 32 = 250.

Over * run rate = runs.
So run rate = 250/40 = 6.25.

Shivu said: (Oct 31, 2016)  
Thank you @Nish.

Rahul said: (Nov 11, 2016)  
x = req run rate.
(10 * 3.2) + (40 * x) = 282,
32 + 40x = 282,
40x = 250,
x = 6.25.

Barun said: (Dec 3, 2016)  
Why is 3*10?

Chahat Sony said: (Dec 26, 2016)  
In the first 15 overs of a one-day cricket match, the run rate was only 6.2 to reach the target of 303 runs in the remaining 35 overs, the run rate should be?

Please solve it.

Siva said: (Jan 5, 2017)  
@Pranav.

Batsman scored 87 runs in his 17th innings as we all know that average is nothing but equal distribution.

So we can say that his increased average should be shared to every innings so 17*3=51 now we can clearly say that if he wants to increase his average he has to score more runs than the previous innings. so answer 87-17 * 3=> 87 - 51 = 36.

Siva said: (Jan 5, 2017)  
@Chahat.

First, 15 overs team scored 120 runs at rate 6.2 and 183 runs need to be scored to reach 303 in 35 overs so req rate is 183/35 = 5.22.

Ritesh Bajaj said: (Jan 10, 2017)  
Why we subtract 282 from (3.2*10) and why we divide the whole thing by 40?

Shiva said: (Jan 29, 2017)  
Run rate for first 10 overs is 3.20.
So 10 * 3.20=30 runs in 10 overs.

40 * how much gives 250 = ??? so that over all become 280.
So,
check from options 40 * 6.25 = 250
250 + 30 = 280

Option A is correct answer.

Renu said: (Feb 16, 2017)  
Super & excellent explanation @Muhundhan.

Bhargavi said: (Mar 2, 2017)  
A batsman makes a score of 87runs in the 17th inning & thus increases his avg by 3. Find his avg after 17th inning? Can anyone solve this problem?

Ali said: (May 2, 2017)  
Thanks @Vinoth M.

Malini said: (May 14, 2017)  
The average weight of 8 men is increased by 1.5 kg when one of the men who weighs of 9 mangoes increases by 20g, if one of them weighing 120g, is replaced by another. The weight of the new mango is?

Please help me to solve the problem.

Deepak said: (Jun 7, 2017)  
10 overs was completed with a run rate of 3.2 for over ....which means they scored 3.2 runs in single overs there for 3.2 x 10 = 32.

Target was 282 so subtract 282 by 32 therefore 282-32 = 250.
250 should be scored in 40 overs.
So, divide 250 by 40.
250/40 = 6.25.

Riddhi said: (Jun 29, 2017)  
282 ie the target run.
10 over + 40 over = 50 over ie in 50 overs 282 should be made in order to win.
So run rate in 50 over needed is 282/50 = 5.64.

USING METHOD OF DEVATION.
3.2--5.64= --2.44*10 = --24.4......deviation for 10 overs (equ 1).
(Let X be avg for next 40 overs).
(X--5.64)*40 = 40X--225.6.......deviation for 40 overs.
(Equ 2)
Solving equ 1 and 2 we get,
40X--255.6--24.4 = 40X--250.
X = 250/40 = 6.25 run rate required in 40 overs.

Kaviya said: (Jul 24, 2017)  
Sum(h+w+c)three years ago:

(x-3)+(y-3)+(y-3)=27*3,
x+y+z=90....................eqn(1),
sum(w+c)five years ago:
(y-5)+(z-5)=20*2.
y+z=50.........................eqn(2).
simplify 1&2.
x=40.............................(ans).

Sh G said: (Aug 31, 2017)  
Thanks @Pratik.

Kavya said: (Sep 1, 2017)  
Super & excellent explanation @Muhundhan.

Shravya said: (Sep 1, 2017)  
Why do we minus 282-(3.2*10)?

Seeramsettykavya said: (Oct 3, 2017)  
What is the logic behind this?

Ram said: (Nov 26, 2017)  
Thanks for the explanation @Deepa.

Mounika said: (Dec 27, 2017)  
Am not understanding this, Please explain in simple way.

Abhishek said: (Apr 22, 2018)  
Why .6.25?

Biswajit said: (Apr 28, 2018)  
Not understanding this, please explain.

Nigus said: (May 10, 2018)  
@Biswaji.

it means ; 10x3.2+40x(x)=282.
so,
32+40x=282,
40x=282-32,
40x=250,
x=250/40,
x=6.25.

Shruti Godi said: (Jun 15, 2018)  
First 10 overs ----> 3.2 runrate.
Remaining 40 overs ----> x runrate.

(10*3.2)+(40*x) = 282,
32+40x = 282,
X = 25/4,
X = 6.25.

Yeri Tazu said: (Jul 14, 2018)  
For 1st 10 over:
3.2=(y/10).

Let y be the run.
y= 32 runs in 10 over.

For next 40 over:
x=(y+282)/50.

This match is talking about 1 day match which is of 50 overs. Also, 10+40=50.

Put value of 'y'
x=(32+282)/50,
x=6.28~6.25(ans).

Hope you understand.

Ganesh said: (Jul 24, 2018)  
3.2*10=32.
282-32=250.
250÷40=6.25.

Brahmin Shrestha said: (Aug 20, 2018)  
Total over of match=10+40=50.
Total runs in 50 overs=282.
First 10 overs runs =3.2*10=32.
We have to calculate run rate of last 40 overs.
Now..run in 40 over= total run-10 over's run.
So, 282-32=250.

Run rate in 40 overs= run in 40 overs ÷overs.
=250÷40=6.25.

Hence, the required run rate in 40 is 6.25 answer.

Leena said: (Aug 21, 2018)  
Nice explanation, thank you.

Red Bull said: (Oct 3, 2018)  
Thanks @Pratik Mehta.

Raja said: (Feb 13, 2019)  
First we have to calculate the last 40 overs run rate.

Total score =282 but already they are scored in first 10 overs score was(10 * 3.2=32),
For these, we are subtracting,
Total score -10 overs score then (282-32) = 250.
Then we have get the score of last 40 over the score was 250.
Total score scored by last 40 overs/ number of overs.
250/40 = 6.25.

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