Latest CTS Aptitude Question SOLUTION: If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by

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If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by

Asked In CTS veer (13 years ago)

Solved ved dhawan Read Solution (5)

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Read Solution (5) :

Ravi B Mali  (13 years ago)

ALGEBRAIC SUM is 5380. the sum varies(increases) by 330.

Solution:
Sum of all numbers from 1 to n is given by n(n+1)/2
so sum of all numbers from 1 to 100 is 100*(100+1)/2 = 5050

6 comes 20times in the numbers from 1 to 100
6 comes in 'units' place 10 times in the numbers 1 to 100 i.e. 6,16,26,....,96
6 comes in 'tens' place 10 times in the numbers 1 to 100 i.e. 60,61,62,.....,69

sum of these 6's is 10(6*10)+10(6*1)=600+60=660

if all 6's are replaced by 9
then sum of those 9's will be 10(9*10)+10(9*1)=990

now algebraic sum will be 5050-660+990= 5380

Is this solution Helpfull? Yes (75) | No (20)  

ved dhawan  (13 years ago)

from 1 to 100, 6 is used 10 time at unit place and 10 times at tenth place so on replaces it by 9 ,its value increased 30(10*3=30)due to unit place and 300 (10*30 = 300) due to tenth place so total increase will be 330

Is this solution Helpfull? Yes (50) | No (3)  

vikash vicky  (9 years ago)

1 11 21 .......91
2 12 22........92
3 13 23........93
. . . .. . .. . .
. . .. .. . .. .
. . .. . . .. . ...
there are total 20 occurrence of 6. once place at 6 th row in every column and tens place in 6 th column
and diff of 6 and 9 is 3 so
3*1*10+3*10*10 = 330

Is this solution Helpfull? Yes (7) | No (3)  

VIVEK  (9 years ago)

4720 ...

Is this solution Helpfull? Yes (4) | No (1)  

RAJASREE.S  (8 years ago)

if all 6 are replaced with 9 from 1 to 100 then algebric sum would varies by 330.
explanation
first take the numbers which have 6 in their unit place - 06,16,26,36,46,56,66,76,86,96.
if all 6 in unit plce is replaced with 9 then in each case the increment would be 3.
so for all ten numbers total increment is 10*3=30.

then take all numbers which have 6 in their tenth place - 60,61,62,63,64,65,66,67,68,69
in each case if we replace 6 with 9 -90,91,92,93,94,95,96,97,98,99
then there is increment of 30 in each case .
so total increment for ten numbers is 10*30==300.
so the total increment including unit and tenth place is 30+300=330

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