Latest CTS Aptitude Question SOLUTION: Consider the sum of first 70 natural numbers.If every digit 6 is replaced by 8 then what would be the net increase and the new sum?

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Consider the sum of first 70 natural numbers.If every digit 6 is replaced by 8 then what would be the net increase and the new sum?

Asked In CTS Meenakshi (9 years ago)

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bavya  (9 years ago)

The sum of first 70 natural numbers 70(70+1)/2 =2485
6,16,26,36,46,56,66 are replaced by
8,18,28,38,48,58,68
and 60.....69 are replaced by 80.....89
hence for unit digits = 7*2=14
tens digit = 10*20=200
net increase is 200+14 =214
new sum is 214+2485=2699

Is this solution Helpfull? Yes (21) | No (3)  

apoorv tiwari  (9 years ago)

The sum of first 70 natural numbers 70(70+1)/2 =2485
6,16,26,36,46,56 are replaced by
8,18,28,38,48,58
and 66 is replace by 88
and 60,61,62,63,64,65,67,68,69 are replaced by 80.....89
hence for unit digits = 6*2=12
and for 66 change in 88 then = 22
tens digit = 9*20=180
net increase is 180+12+22 =214
new sum is 214+2485=2699

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Praveen Kumar Soni  (9 years ago)

Sorry hena but i think u didnt took 66 in consideration for the Tens Digit.

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hena samanta  (9 years ago)

sum of first 70 natural numbers=70(70+1)/2=2485
6,16,26,36,46,56,66 are replaced by
8,18,28,38,48,58,68
sum of first digits is 252
sum of second digits is 266
the net increase will be (266-252)=14
the new sum will be 2485-252+266=2499

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Praveen Kumar Soni  (9 years ago)

For n natural no. sum the formulae is n(n+1)/2 so therefore the sum be 35(71) = 2485 n according to question there is replacement of 6 with 8 , within 70 natural no there are 6,16,26,36,46,56,66 and in these, for each unit digit replacement will increase it by 2 ,hence 7*2 = 14 and there is a ten digit replacement for 6 i.e (66 )for one time therefore an addition of 20 more to the sum i.e overall addition of 14+20 = 34 ,so net increase of 34 with the new sum as (2485 + 34 = 2519).

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gopinath.s  (9 years ago)

sry henna u replaced that 66 into 68,bt u shd make 88

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M.AZHAGUVIDHYA  (8 years ago)

sum of the first 70 natural numbers= n/2*(first term+last term)
we know that natural numbers 1,2,3,....70
sum=70/2*(1+70) => 35*71=2485.
every digit is replaced by 6 means 1 to 9 will be 6.
10 to 70 will be 66
=> (6*9)+ (66*61)= 4026
It is incremented by 1595.

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vaibhav vatsal   (7 years ago)

To answer this question, you need to know the simple formula for sum of first 'n' natural numbers which is n (n+1)/2.
Hence sum of numbers from 1 to 70 would be 70X71/2 = 2485.
If every '6' digit is replaced by '8' there would be totally 8 replacements at (6,16,26,36,46,56,60,66). Every replacement will add an additional '2' to the net sum. Hence the new sum will be 2485 + 8 X 2 = 2501 and the increase will be 16.

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