Sujeet got 50 from his father and 25 from his mother. He distributed the whole amount equally among 5 persons. How much did each of them get ? Write mathematical expression and solve it.
Answers
Answer:
Here,
Let N represent no of mangoes.
Then, analyzing the question we can write,
N=2a + 1
N=3b + 2
N=4c + 3
N=5d + 4
N=6e + 5
N=7f
Add 1 on both sides in all the equations. Then,
N+1=2a + 2=2(a+1)
Similarly,
N + 1=3(b +1)
N + 1=4(c +1)
N + 1=5(d +1)
N + 1=6(e +1)
N + 1=7f + 1
This means when that number is increased by 1,it is divisible by 3,4,5, and 6. The second least number divisible by 3, 4, 5 and 6 is 120. We ignore least no 60 as 59 is not divisible by 7. So the number N +1 should be 120x where x is any positive integer.
Take least value of n so that N + 1=120
So, N=120-1=119.
So 119 is the answer.
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Sujit Menon, Scientist/Engineer @ Indian Space Research Organization
Updated December 27, 2014 · Author has 286 answers and 1.5M answer views
You could solve this problem with a simple piece of C code:
#include<stdio.h>
int main()
{
int n;
for(n=7;;n=n+7) // We are incrementing in steps of 7 because we know that the number is divisible by 7. Thanks to a fellow Quoran.
{
if(n%2==1 && n%3==2 && n%4==3 && n%5==4 && n%6==5 && n%7==0)
{
printf("%d\n",n);
break;
}
}
return 0;
}
The answer is 119.
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Tanmay Pandit, Computer Science student at IIT Jodhpur(2022)
Answered February 16, 2016 · Author has 595 answers and 1.7M answer views
Let there be x mangoes in the basket.
From given information, we can infer that x when divided by 2, 3, 4, 5 or 6 leaves a remainder -1 & is a multiple of 7.
Firstly, let's find the LCM of 2, 3, 4, 5 & 6 which comes out to be 60.
Now, x = 60n - 1 where n is a whole number.
We have:
(60n-1)mod7=0.
(4n-1)mod7=0 as 60mod7=4.
Here, least possible value of n is 2.
x =-60(2)-1=120-1=119.
There are 119 mangoes in the basket.
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Parinit Agarwal, works at Deloitte
Answered December 24, 2014 · Author has 125 answers and 696.2K answer views
Thanks for the A2A!
So as per the question, we know that number of mangoes is a multiple of 7 and an odd number (as divided by 2 will leave a remainder of 1)
so N=7x, where x is odd
also, it should not be divisible by 3 or 4 or 5 (as the result is not divisible by these either)
there for x has to be a prime number
so possible values of x are 7,11,13,17...
i.e.
N = 49, 77, 91, 119...
of the above, 119 satisfies the given conditions. hence, the answer is 119
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· Answer requested by Navneet Hindustani
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Arpit Jain, Programmer, Gamer, Thinker
Answered March 18, 2015
It's Simple,
To find the lowest such number, take the LCM (Lowest common multiple) of 2,3,4,5,6 and subtract 1 from it.
Since the number must be divisible by 7, we must use another multiple of the above LCM
This can be formulated as (LCM(2,3,4,5,6)*n)-1 and the minimum "n" which makes the result divisible by 7 is 2
so the answer is 60*2 - 1 = 119
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Parivarthan Reddy, 3D printing enthusiast
Answered December 24, 2014
119
N=7a
N=6b+5
N=5c+4
N=4d+3
N=3e+2
N=2f+1
I wrote a code for this by keeping the condition that a,b,c,d,e,f should be integers, and incrementing 'a' value by 1 for every iteration. It returned 'a' value as 17.
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