Question

the ratio of number of boys or she number of girls in a school of 1440 students is 4:5 if 40 new boys are admitted find how many new girls may be admitted to make this ratio 4:3​

Answer 1

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Given :

☞ Total students = 1440.

☞ Ratio = 4 : 5

☞ Changed Ratio = 4 : 3 = 4 / 3

According to the question :

☞ Let No. of. boys = 4a

☞ No. of. girls = 5a

=> 4a + 5a = 1440

=> 9a = 1440

=> a = 1440 / 9

=> a = 160.

☞ So, No. of. Boys = 160 × 4 = 640

☞ No. of. Girls = 160 × 5 = 800.

Let, ' b ' be the No. of. new girls :

☞ Changed Ratio = Boys + New boys / Girls + New girls.

=> 4 / 3 = 640 + 40 / 800 + b

=> 4 ( 800 + b ) = 3 ( 640 + 40 )

=> 3200 + 4b = 1920 + 120

=> 3200 + 4b = 2040

=> 3200 - 2040 = 4b

=> 4b = 1160

=> b = 1160 / 4

=> b = 290.

Therefore,New Girls = 290.

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Answer 2

Question:-

the ratio of number of boys to number of girls in a school of 1440 students is 4:5 if 40 new boys are admitted find how many new girls may be admitted to make this ratio 4:3 .

Solution:-

Given:- a) the ratio of number of boys to number of girls in a school of 1440 students is 4:5

b) 40 new boys are admitted

c) girls may be admitted to make this ratio 4:3

Find:- how many new girls may be admitted to make this ratio 4:3

So now,{ From given ( a ) }

By ratio of boys to girls.

let, boy's be 4x .......... ( 1 ) &

girl's be 5x ............. ( 2 )

so, total number of student's 1440

means,

=> 4x + 5x = 1440

=> 9x = 1440

=> x = 1440/9

=> x = 160

so, put value of x in ( 1 ) & ( 2 )

=> boy's = 4x = 4 ( 160 ) = 640 ..( 3 )

=> girl's = 5x = 5 ( 160 ) = 800 ..( 4 )

so, now { From given ( b ) & ( c ) }

Add 40 to ( 3 )

=> boy's = 640 + 40 = 680 ......( 5 )

Let G be girl's so,

=> girl's = 800 + G ......... ( 6 )

To Find the new ratio of

boy's to girl's ( is 4:3 )

{we can wrote ratio 4:3 in a from of

numerator and denominator ( 4/3 )}

now { from ( 5 ) & ( 6 ) }

=> 4/3 = 680/(800 + G)

=> 4 ( 800 + G ) = 3 ( 680 )

=> 3200 + 4G = 2040

=> 4G = 2040 - 3200

=> 4G = - 1160

=> G = - 1160/4

=> G = - 290

Hence, 290 girl's neglected or substracted from 800 girl's then

we got ratio of boy's to girl's is 4:3

so here

=> girl's = 800 - 290 = 510 ..... ( 7 )

Now { From ( 5 ) & ( 7 ) }

=> boy's/girl's = 680/510 = 4/3

or 4:3

Hence, 680 boy's & 510 girls in school if ratio of boy's to girl's is 4:3

i hope it helps you.