Question

The number of students in school A, B and C are in a ratio of 5 : 4 : 8 respectively. If the number of students is increased by 40%, 75% and 25% respectively in next year and the total students after increment is 1200, what was the total number of students initially?​

Answer 1

Step-by-step explanation:

Correct option is

A

18:23:21

The ratio of the number of students studying in school A, B, C.

=6:8:7

Suppose number of student's in school

A=6x

B=8x

C=7x

It will be Increased by

A=6x+6x×20 %

=6x+

100

6x×20

=6x+

5

6x

=

5

30x+6x

=

5

36x

B=8x+

100

8x×15

=8x+

5

6x

=

5

46x

C=7x+

100

7x×20

=

5

35x+7x

=

5

42x

New Ratio =

5

36x

:

5

46x

:

5

42x

=36:46:42

=18:23:21

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Answer 2

Given:

Ratio of students in School A, B, and C $=5:4:8$.

Percentage increase of students in School A, B, C are 40%, 75% and 25% respectively.

Total students after increment$=1200$

To find: Total number of students initially.

Solution:

Know that from the question,

The ratio of the number of students studying in school A, B, C $=6:8:7$

Assume that the number of student's in school,$A=6x, B=8x, C=7x$

Understand that,

The number of increase in students in School A is,  

 $A'=5x+5x\times40\%$

$\Rightarrow A'=5x+\frac{40}{100} \times5x$

$\Rightarrow A'=5x+2x\\\Rightarrow A'=7x$

The number of increase in students in School B is,  

 $B'=4x+4x\times75\%$

$\Rightarrow B'=4x+\frac{75}{100} \times4x$

$\Rightarrow B'=5x+3x\\\Rightarrow B'=8x$

The number of increase in students in School C is,  

 $C'=8x+8x\times25\%$

$\Rightarrow C'=8x+\frac{25}{100} \times8x$

$\Rightarrow C'=8x+2x\\\Rightarrow C'=10x$

Find the value of x.

$7x+8x+10x=1200\\\Rightarrow 25x=1200\\\Rightarrow x=\frac{1200}{25}\\\RIghtarrow x=48$

Find the total number of students in school A initially.

$A=6x, \\\RIghtarrow A=6\times48\\\Rightarrow A=288$

Find the total number of students in school B initially.

$B=8x\\\Rightarrow B=8\times48\\\Rightarrow B=384$

Find the total number of students in school C initially.

$C=7x\\\Rightarrow C= 7\times48\\\Rightarrow C=336$

Find the total number of stuidents in Schools A, B, and C initially.

$288+334+336=958$

Hence, there is a total of 958 students initially.