100 Bananas

A man ate 100 bananas in five days, each day eating 6 more than the previous day. How many bananas did he eat on the first day?
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Editorial / Best Answer

vijay pal saharan  

  • Member Since Mar-2009 | Mar 25th, 2009


Let the number of bananas he ate first day be x.
then x+x+6+x+12+x+18+x+24=100

=>5x+60=100
=>5x=40
x=8
that is, he ate 8 bananas on first day.

Showing Answers 1 - 3 of 3 Answers

neerajviku

  • Feb 10th, 2009
 

LET THE BANANA EATEN ON FIRST DAY BE X-12

         THEN ON FOLLOWING DAY MAN ATE         X-6  , X  ,x+6  , X+12

    Then total banana eaten during  five day is


     x-12+x-6+x+x+6+x+12=100
   =>  5x=100
   =>  x=20

  so,banana eaten on first day is 20-12=8

shona_

  • Nov 28th, 2009
 

Let x be no of banans he ate on first day.
then on the next day he ate x+6,x+12,x+18,x+24
so x+x+6+x+12+x+18+x+24=100
so 5x+60=100
x=8
so he ate 8 banans on first day

Let, he ate 'x' bananas 1st day. then next four days he eats as following.
x+6, x+12, x+18 and x+24
hence, by summing all these we get,
x+x+6+x+12+x+18+x+24=100
=> 5x+60=100
=> 5x=40
=> x=8
Hence, a man ate '8' bananas on 1st day

All the best for your career

indiran1987

  • Dec 28th, 2009
 

1st day                  = 08
2nd day (8+6)      = 14
3rd day (14+6)    = 20
4th day (20+6)    = 26
5th day (26+6)    = 32
Total                     = 100

It can be considered as an arithmetic progression with first term a, common difference d=6, number of terms n=5, sum of first five terms=100.

n/2*(2a+(n-1)*d)=100;
5/2*(2a+4*6)=100;
a+12 =20;
a=20-12
= 8;

In the best rated answer there is a serious error;  5x =40; then how can x be 6;



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Robin jha

  • Jan 15th, 2010
 

Answer is 8 bananas

Let suppose he eat x banana on first day, then
2nd day he eat x+6 banana
3rd day he eat x+12 banana
4th day he eat x+18 banana
and 5th day he eat x+24 banana
Hence from above
x+(x+6)+(x+12)+(x+18)+(x+24)=100
5x+60=100
5x=40
x=8

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As discussed earlier, there are two ways to find out the answers. We can use either
n*a+n(n-1)6/2= Given number ( here it is 100) or your can use AP method using x+(x+6)+..... However, 8 is the right answer.

Using First Method,

5*a+5(5-1)6/2=100
=>5a+5(4)*6/2=100
=>5a+20*6/2=100
=>5a=100-60
=>a=40/5=8

8 is the right answer

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anandjain

  • Feb 1st, 2010
 

Let the bananas ate I day be x 
then no of banas eaten each are in AP and last term will be x+24
so applying formula for sum of terms of AP
Sn=100=5/2(x+(x+24))
x=8

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5 days, each day 6 bananas more than previous i.e
6 12 18 24 30
Sum comes out to be  90
i.e more ten bananas for 5 says...add 2 bananas for each day
ie
8 14 20 26 32
Therfore 1st day 8 bananas.

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i4unishant

  • Mar 12th, 2010
 

Let, 'x' be the number of bananas he ate on 1st day, then next four days he eats as following.
x+6, x+12, x+18 and x+24
by summing all these we get,
x+x+6+x+12+x+18+x+24=100
=> 5x+60=100
=> 5x=40
=> x=8
The man ate '8' bnanas on 1st day.

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mmukundan

  • Apr 13th, 2010
 

Let he eats x bananas on 1st day
2nd day x+6 and 3rd day x+6+6= x+12 bananas so it forms an arithmetic progression

Sum of this ap = 100

ie n/2(1st term + last term) = 100
n=5, 1st term = x, and last term = a+(n-1) d = x+ 4*6 = x+24 since d=6
ie 5/2(x+x+24) = 100
    5(x+12) = 100
      x+12 = 20
      x = 8

hmvasista

  • Apr 29th, 2010
 

This forms an AP(arithmatic progression)

the summation of such a series is
S=(n/2)(2a+(n-1)d)
n-> no of terms, d->difference,a->initial term

substituting we get, S=100, n=5,d=6 so a=5

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Lets Say man ate X bananas on Day1 so


Day2 --> X+6
Day3 --> X+12
Day4 --> X+18
Day5 --> X+24

As we know he ate total 100 bananas in 5 days

so X+X+6+X+12+X+18+X+24 = 100

5X+60=100
5X=40
X=8

So he ate 8 Bananas on Day 1

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Let x be number bananas ate per day
then next day x+6
next day x+12,x+18,x+24
and its total equal to 100
i.e
x+x+6+x+12+x+18+x+24=100
5x+60=100
x=8
so 8 bananas per day

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hydsarema

  • Jun 9th, 2010
 

Let the number of bananas a man ate on the first day be x,

then x,x+6,x+12.........  is in arithmatic progression with commom difference 6.
so d=6 and  n=5;

the sum of first n finite terms in AP is sn=(n/2)(2a+(n-1)d)
here sn=100

100=(5/2)(2a+4*6)
a=8

where a is the first term in AP

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darkgreen

  • Jun 9th, 2010
 

Let x be the bannas he ate in 1st day. so,

x+x+6+x+12+x+18+x+24=100
5x+60=100
x=8.
so the bananas eaten by him in 1st day is 8. 

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90306

  • Jul 1st, 2010
 

first day = "x" bananas                           

2nd day  = x+6 
3rd day   = x+12
4th day   = x+18
5th day    = x+24
 
 in five days he ate 100 bananas, so

x+x+6+x+12+x+18+x+24=100
5x+60=100
5x=100-60
5x= 40 therefore x = 8 bananas

proof: 8+14+20+26+32=100
hence prooved

 

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RAHUL CHANDAK

  • Aug 14th, 2011
 

8

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KAPIL

  • Aug 26th, 2011
 

On first day he will eat 8 bananas next day 14 then 20 then 26 and last day he will eat 32 bananas then the total will come
8+14+20+26+32=100

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rakend raj

  • Aug 30th, 2011
 

8 bananas on the first day..

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U.MONICA DEVI

  • Sep 10th, 2011
 

he had a chance to eat 76 bananas in first day coz he ate 100 bananas in 5 days n each day he increased his stuff by eating extra 6 day by day

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selva

  • Aug 12th, 2015
 

8

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Dhivya

  • Aug 14th, 2015
 

8

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