Latest L&T Aptitude Question SOLUTION: 26. 16 grams of radioactive material decays into 8 grams in 10 years. How long will it take to decay to 1 gram? Ans: 70 yrs

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26. 16 grams of radioactive material decays into 8 grams in 10 years. How long will it take to decay to 1 gram?
Ans: 70 yrs

Asked In L&T (12 years ago)

Unsolved Read Solution (9)

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Rakesh Kumar Kohli  (12 years ago)

Ans. 40years

This radioactive material has half life after 10 years.

16 grams decays into 8 grams in 10 years.
Then 8 grams decays into 4 grams in next 10 years.
Then 4 grams decays into 2 grams in next 10 years.
Then 2 grams decays into 1 gram in next 10 years.
Thus 16 grams decays into 1 gram in 40 years.

Is this solution Helpfull? Yes (56) | No (15)  

Anna  (9 years ago)

it is not mentioned that it will decay in exact half so we cant say 40 years.
answer will be 70 year.

16 gm reduced to 8gm in 10yrs
so 8 gm get decayed
for decaying 1 gm it takes 10/8 yrs
for decaying 8 gm it takes 10/8*8

remaining 8 gm
need to decay 7 to get 1 gm remaining
for decaying 7 it takes
10/8*8*7
=10*7
=70 years

Is this solution Helpfull? Yes (5) | No (2)  

Chetan Anand  (12 years ago)

Ans will be 80 years.
Radioactive material decays 8 grams in 10 years. Then,
4 grams in 20 years
2 grams in 40 years
1 gram in 80 years.

Is this solution Helpfull? Yes (4) | No (35)  

sanchita  (9 years ago)

ans:70
16gm decays into 8gm in 10y
so 8gm decays into 4gm=8/2=4*10=40
4gm decays into 2gm=4/2=2*10=20
2gm decays into 1gm=2/2=1*10=10
so 40+20+10=70

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Chiranjeevi Y  (10 years ago)

16---------8------>10
8----------4------>10
4----------2------->10
2----------1------->10

so ans is 40yrs

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Sumit Gawade  (9 years ago)

Ans . 70 yrs

16 gms to 8 gms in 10 yrs
so.
1 gms = 10/8 yrs
4 gms = 4*(10/8) = 5
2 gms = 2*(10/8) = 5/2
1 gms = 1*(10/8) = 5/4

on adding
5+(5/2)+(5/4)
= (40+20+10)/8
= 70/8

so it takes 70 yrs to decay 8 grms to q grms

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prathamesh dinkar  (8 years ago)

Rate of decay is directly proportioal to mass present at that time.
dm/dt =-k*m (m= mass)
by integrating, we get,

ln(mi/mf)=kt+constant mi=initial mass and mf=final mass

at t=0,mi=mf so constant=0
and t=10years, mf=8 so, k=ln(2)/10

now mf=1
so, ln(16)=ln(2)*t/10
hence time=40years !!

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sravani  (9 years ago)

10y 10y 10y 10y
16---------8 -------------4---------------2---------------1
total no.of years =40years...
I think the answer is wrong...

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ganesh shinde  (9 years ago)

i think 18-19 yrs

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