Question

A jar was full with honey. A person used to draw out 20% of the honey from the jar and replaced it with sugar solution. He has repeated the same process 4 times and thus there was only 512 gm of honey left in the jar, the rest part of the jar was filled with the sugar solution. The initial amount of honey in the jar was filled with the sugar solution. The initial amount of honey in the jar was:

A) 1.25 kg B) 1 kg C) 1.5 kg D) None of these

Answer 1

Answer:

The initial amount in the jar is 1250 gm.

Step-by-step explanation:

Given : A jar was full with honey. a person to drawn out 20% of the honey from the jar and replaced it with sugar solution. he done the same process 4 times and thus there was only 512 gm of honey left in the jar, the rest part of the jar was filled with the sugar solution.

To find : The initial amount of honey in the jar was ?

Solution :

The amount of honey left in the jar = 512 gm

Let the initial amount of honey = x gm

Then according to question,

512=x \times (1-20\%)^4512=x×(1−20%)

4

512=x \times (1-\frac{20}{100})^4512=x×(1− 10020)

512=x \times (\frac{100-20}{100})^4512=x×(

100

100−20 )

4

512=x \times (\frac{80}{100})^4512=x×(

100

80

)

4

512=x \times (\frac{4}{5})^4512=x×(

5

4

)

4

512=x \times 0.4096512=x×0.4096

\frac{512}{0.4096}=x

0.4096

512

=x

x=1250x=1250

Therefore, The initial amount in the jar is 1250 gm.

Answer 2

Percentage

Let the maximum capacity of jar be $100x$.

Percentage of honey he used to exchange with the help of sugar solution is $20\%$.

Number of times he did repeated the process is 4.

Quantity of honey left in the jar is 512gm.

According to question,

$512=100x[1-\frac{20}{100}]^4\\ \\\implies 512=100x[\frac{80}{100}]^4\\\\\implies 512=100x [\frac{4}{5}]^4\\\\\implies 512\times625=100x\times256\\\\\implies1250=100x$

$100x$  is the capacity of jar which means $1250 \gm=1.25 \ kg$.

Hence, 1.25 kg is the capacity of the jar.