In a row of boys facing north, Amit is 26th from the left while Rajan is 14th from the right. Amit is sitting to the left of Rajan. If the number of boys between them is one-third of the total number of boys in the line. What is the total number of boys in the row? a. 40 b. 30 c. none of these d. 50
Question
In a row of boys facing north, Amit is 26th from the left while Rajan is 14th from the right. Amit is sitting to the left of Rajan. If the number of boys between them is one-third of the total number of boys in the line. What is the total number of boys in the row?
a. 40
b. 30
c. none of these
d. 50
Solution
To solve this problem, we need to follow these steps:
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We know that Amit is 26th from the left and Rajan is 14th from the right. So, without considering the boys between them, there are already 26 + 14 = 40 boys.
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The problem states that the number of boys between Amit and Rajan is one-third of the total number of boys in the line. Let's denote the total number of boys as x. Therefore, the number of boys between Amit and Rajan is x/3.
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We can set up the equation: 40 + x/3 = x.
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To solve for x, we first multiply every term by 3 to get rid of the fraction: 120 + x = 3x.
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Then, we subtract x from both sides to isolate 3x on one side: 120 = 2x.
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Finally, we divide both sides by 2 to solve for x: x = 60.
So, the total number of boys in the row is 60. The correct answer is (c) none of these.
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