
Divide 240 into three parts so that of the first, of the second and of the third part are equal.
Answer
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Hint: Here, we will first write the given statement mathematically by assuming the three parts to be some variable. Then we will add all the parts and equate it to 240. We will use the mathematical equation formed by us to substitute the values of the second and third parts in terms of the first part. Hence, we will find the value of one variable. Substituting further, we will get the value of each part and hence, we will be able to find the required answer.
Complete step-by-step answer:
Let the three parts be and .
Now, according to the question,
The number 240 is divided into three parts so that of the first, of the second and of the third part are equal.
Hence, if the first part is , second part is and the third part is , then, we can say that,
of is equal to of is equal to of
Now, writing this mathematically, we get,
……………………………..
Now, we will write every part in terms of .
Hence, the first part will remain the same, i.e.
From equation , we can say that,
Hence, by cross multiplying,
Therefore, the second part …………………………
Again, from equation , we get
Hence, by cross multiplying,
Therefore, the third part …………………………………
Now, since we have divided the number 240 into three parts i.e. and .
Hence, the summation of these parts will give us the number 240
Here, substituting and from and , we can write this as:
Now, taking the LCM as 3 in the LHS,
Now, solving further, we get,
Dividing both sides by 4,
Therefore, the first part
Hence, the second part
And, the third part
Therefore, we should divide 240 into 60, 80 and 100 if we want that of the first, of the second and of the third part are equal.
Hence, this is the required answer.
Note: In order to check whether we have divided the given number correctly or not, we can substitute the values in i.e.
This is the statement which is required to be proved.
Hence, if the three parts, in which we have divided 240, satisfies this equality, then our answer is correct.
Therefore, substituting , and , we get,
Clearly, they are equal.
Hence, it is proved that 240 should be divided as 60, 80 and 100 if we want that of the first, of the second, and of the third part are equal.
Hence, this is the required answer.
Complete step-by-step answer:
Let the three parts be
Now, according to the question,
The number 240 is divided into three parts so that
Hence, if the first part is
Now, writing this mathematically, we get,
Now, we will write every part in terms of
Hence, the first part will remain the same, i.e.
From equation
Hence, by cross multiplying,
Therefore, the second part
Again, from equation
Hence, by cross multiplying,
Therefore, the third part
Now, since we have divided the number 240 into three parts i.e.
Hence, the summation of these parts will give us the number 240
Here, substituting
Now, taking the LCM as 3 in the LHS,
Now, solving further, we get,
Dividing both sides by 4,
Therefore, the first part
Hence, the second part
And, the third part
Therefore, we should divide 240 into 60, 80 and 100 if we want that
Hence, this is the required answer.
Note: In order to check whether we have divided the given number correctly or not, we can substitute the values in
This is the statement which is required to be proved.
Hence, if the three parts, in which we have divided 240, satisfies this equality, then our answer is correct.
Therefore, substituting
Clearly, they are equal.
Hence, it is proved that 240 should be divided as 60, 80 and 100 if we want that
Hence, this is the required answer.
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