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Chapter 18: Problem 745

A student obtain \(75 \%, 80 \%\) and \(85 \%\) in three subjects. If the marks of another subject are added then his average cannot be less then (a) \(60 \%\) (b) \(65 \%\) (c) \(80 \%\) (d) \(90 \%\)

Short Answer

Expert verified
The lowest possible average the student can obtain is \(75\%\) which is achieved when the student scores a minimum of \(60\%\) in the fourth subject. Therefore, the answer is (a) \(60 \%\) in the fourth subject.

Step by step solution

01

Calculate the total percentage of the first three subjects.

To do this, simply add the percentages together: \(75\% + 80\% + 85\% = 240\%\).
02

Consider the first option (60%).

If the student scores a minimum of 60% in the fourth subject, the total percentage would be \(240\% + 60\% = 300\%\). Now, to find the average percentage, divide the total percentage by 4 (number of subjects): \(300\% ÷ 4 = 75\%\).
03

Consider the second option (65%).

If the student scores a minimum of 65% in the fourth subject, the total percentage would be \(240\% + 65\% = 305\%\). Now, to find the average percentage, divide the total percentage by 4 (number of subjects): \(305\% ÷ 4 = 76.25\%\).
04

Consider the third option (80%).

If the student scores a minimum of 80% in the fourth subject, the total percentage would be \(240\% + 80\% = 320\%\). Now, to find the average percentage, divide the total percentage by 4 (number of subjects): \(320\% ÷ 4 = 80\%\).
05

Consider the fourth option (90%).

If the student scores a minimum of 90% in the fourth subject, the total percentage would be \(240\% + 90\% = 330\%\). Now, to find the average percentage, divide the total percentage by 4 (number of subjects): \(330\% ÷ 4 = 82.5\%\).
06

Compare the calculated averages.

It was found that if the student scores a minimum of (a) 60%, the average would be 75%; (b) 65%, the average would be 76.25%; (c) 80%, the average would be 80%; and (d) 90%, the average would be 82.5%. Based on these calculations, the lowest possible average is 75%, which is achieved when the student scores a minimum of 60% in the fourth subject. Answer: (a) \(60 \%\).

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Most popular questions from this chapter

A box contain 4 red and 3 black ball. One ball is taken away from the box. After that two balls are drawn at random and both found red, what is the probability that the first ball taken always was also red? (a) \((2 / 5)\) (b) \((4 / 7)\) (c) \((24 / 105)\) (d) None

Three unbiased dice are tossed. Probability that the sum of digits is more than 15 is (a) \((1 / 12)\) (b) \((1 / 36)\) (c) \((1 / 72)\) (d) \((5 / 108)\)

Standard deviation of two observations is \(3.5\), one observation is 3 then second observation is (a) 9 (b) 10 (c) 7 (d) 3

The mean of the numbers \(a, b, 8,5,10\) is 6 and the variance is \(6.80\) then which one of following gives possible values of a and \(b\) ? (a) \(a=3, b=4\) (b) \(a=0, b=7\) (c) \(a=5, b=2\) (d) \(a=1, b=6\)

If the mean of the set of numbers \(x_{1}, x_{2}, \ldots \ldots \ldots x_{n}\) is \(\underline{x}\) then the mean of the numbers \(x i+2 i, 1 \leq i \leq n\) is (a) \(\underline{x}+2 n\) (b) \(\underline{x}+n+1\) (c) \(\underline{x}+2\) (d) \(\underline{x}+n\)
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