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Divide ₹ 1400 into three parts in such a way that half of the first part, one-fourth of the second part and one-eighth of the third part are equal.
- a)300, 600, 500
- b)200, 400, 800
- c)100, 400, 1000
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Divide 1400 into three parts in such a way that half of the first par...
Solve this question using options. 1/2 of the first part should equal 1/4th of the second part and 1/8th of the third part. Only, option (b) satisfies these conditions thus this option is correct
Most Upvoted Answer
Divide 1400 into three parts in such a way that half of the first par...
To solve this problem, we need to divide 1400 into three parts in such a way that half of the first part, one-fourth of the second part, and one-eighth of the third part are equal.
Let's assume the three parts are x, y, and z.
According to the given condition, we have the following equations:
1) (1/2) * x = (1/4) * y = (1/8) * z
2) x + y + z = 1400
Now, let's solve these equations step by step:
1) (1/2) * x = (1/4) * y = (1/8) * z
From this equation, we can find the ratio of x, y, and z:
x:y:z = 1/2 : 1/4 : 1/8
= 4/8 : 2/8 : 1/8
= 4 : 2 : 1
So, the three parts are in the ratio of 4:2:1.
2) x + y + z = 1400
Using the ratio from the previous step, we can write this equation as:
4k + 2k + k = 1400
7k = 1400
k = 200
Now, substituting the value of k back into the ratio, we get:
x = 4k = 4 * 200 = 800
y = 2k = 2 * 200 = 400
z = k = 200
So, the three parts are 800, 400, and 200.
Therefore, the correct answer is option 'B': 200, 400, 800.
In this way, we have successfully divided 1400 into three parts such that half of the first part, one-fourth of the second part, and one-eighth of the third part are equal.
Let's assume the three parts are x, y, and z.
According to the given condition, we have the following equations:
1) (1/2) * x = (1/4) * y = (1/8) * z
2) x + y + z = 1400
Now, let's solve these equations step by step:
1) (1/2) * x = (1/4) * y = (1/8) * z
From this equation, we can find the ratio of x, y, and z:
x:y:z = 1/2 : 1/4 : 1/8
= 4/8 : 2/8 : 1/8
= 4 : 2 : 1
So, the three parts are in the ratio of 4:2:1.
2) x + y + z = 1400
Using the ratio from the previous step, we can write this equation as:
4k + 2k + k = 1400
7k = 1400
k = 200
Now, substituting the value of k back into the ratio, we get:
x = 4k = 4 * 200 = 800
y = 2k = 2 * 200 = 400
z = k = 200
So, the three parts are 800, 400, and 200.
Therefore, the correct answer is option 'B': 200, 400, 800.
In this way, we have successfully divided 1400 into three parts such that half of the first part, one-fourth of the second part, and one-eighth of the third part are equal.
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Divide 1400 into three parts in such a way that half of the first part, one-fourth of the second part and one-eighth of the third part are equal.a)300, 600, 500b)200, 400, 800c)100, 400, 1000d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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