In a batch of 80 students, 30% scored more than 70% and 80% scored more than 40% in an exam. If 15% of the students scored less than 30%, how many students scored between 15 to 35 marks if the total marks were 50?

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Solution

The correct option is C 44
$T o t a l m a r k s = 50$

$∴ 15 m a r k s = \frac{15}{50} = \frac{30}{100} = 30 % o f t h e t o t a l$

Similarly,

$35 m a r k s = \frac{35}{50} = \frac{70}{100} = 70 % o f t h e t o t a l$

Hence, the students who scored between 15 and 35 marks are the same as the ones who scored between 30% and 70%.

$S t u d e n t s w h o s c o r e d b e t w e e n 30 % t o 70 %$

$= T o t a l s t u d e n t s - (S t u d e n t s b e l o w 30 % + S t u d e n t s a b o v e 70 %)$

Now,

$T o t a l n u m b e r o f s t u d e n t s = 80$

$S t u d e n t s w h o s c o r e d m o r e t h a n 70 %$
$= 30 % o f 80 = \frac{30}{100} \times 80 = 24$

$S t u d e n t s w h o s c o r e d l e s s t h a n 30 %$
$= 15 % o f 80 = \frac{15}{100} \times 80 = 12$

$⟹ S t u d e n t s w h o s c o r e d b e t w e e n 30 % a n d 70 %$
$= 80 - (24 + 12)$
$= 44$

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Similar questions

There are 68 students of 9th standard from model Highschool, Nandpur. They have scored following marks out of 80, in written exam of mathematics.

70, 50, 60, 66, 45, 46, 38, 30, 40, 47, 56, 68, 80, 79, 39, 43, 57, 61, 51, 32, 42, 43, 75, 43, 36, 37, 61, 71, 32, 40, 45, 32, 36, 42, 43, 55, 56, 62, 66, 72, 73, 78, 36, 46, 47, 52, 68, 78, 80, 49, 59, 69, 65, 35, 46, 56, 57, 60, 36, 37, 45, 42, 70, 37, 45, 66, 56, 47

By taking classes 30-40, 40-50, .... prepare the less than type cumulative frequency table

Using the table, answer the following questions :

(i) How many students, have scored marks less than 80 ?

(ii) How many students have scored marks less than 40 ?

(iii) How many students have scored marks less than 60 ?

By using data in example (6), and taking classes 30-40, 40-50... prepare equal to or more than type cumulative frequency table and answer the following questions based on it.

(i) How many students have scored marks 70 or more than 70 ?

(ii) How many students have scored marks 30 or more than 30 ?

How many students scored more than or equal to 30 out of 50 marks in a class.
$\begin{matrix} M a r k s & N u m b e r o f s t u d e n t s 0 - 10 & 2 10 - 20 & 12 20 - 30 & 21 30 - 40 & 8 40 - 50 & 5 \end{matrix}$

The final marks obtained in Mathematics by $40$ students are as follows: $60, 56, 90, 50, 62, 67, 100, 48, 39, 70, 60, 55, 68, 58, 59, 98, 84, 78, 60, 37, 64, 52, 77, 48, 61, 88, 58, 44, 75, 53, 62, 75, 82, 61, 19, 49, 39, 68, 50, 52 .$

How many students scored more than $70$ marks?

Q. The given histogram represents marks of the students in mathematics.

What percentage of students scored more than or equal to 40 marks and less than 70 marks?

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