There are 40 members in a students council in a school and the ratio of the number of boys to the number of girls is 3 : 1. How many more girls be added to the council to make the ratio of boys to girls 3 : 2?My answer for this question is coming 6 but it is given as 10.Please clarify where I m going wrong.

Asked by savi1405 | 10th Jun, 2016, 10:22: PM

Expert Answer:

begin mathsize 12px style I n i t i a l l y comma space t h e space r a t i o space o f space b o y s space t o space g i r l s space i s space 3 colon 1.
S u p p o s e space t h e r e space a r e space 3 a space b o y s space a n d space a space g i r l s.
S o space 3 a plus a equals 4 a equals 40
rightwards double arrow a equals 10.
S o space i n i t i a l l y comma space n u m b e r space o f space g i r l s space i s space 10 space a n d space n u m b e r space o f space b o y s space i s space 3 a equals 30.

N o w comma space w e space h a v e space t o space a d d space s o m e space g i r l s.
S u p p o s e space w e space a d d space K space n u m b e r space o f space g i r l s.
S o space n o w space t o t a l space n u m b e r space o f space g i r l s space i s space 10 plus K.
T h e space n u m b e r space o f space b o y s space r e m a i n s space t h e space s a m e colon space 30.
S o space t o t a l space n u m b e r space o f space s t u d e n t s space i s space 10 plus K plus 30 equals 40 plus K
G i v e n space t h a t comma space t h e space n e w space r a t i o space o f space b o y s space t o space g i r l s space i s space 3 colon 2
H e n c e comma space fraction numerator 30 over denominator 10 plus K end fraction equals 3 over 2
rightwards double arrow 30 cross times 2 equals 3 open parentheses 10 plus K close parentheses
rightwards double arrow 60 equals 30 plus 3 K
rightwards double arrow 3 K equals 30
rightwards double arrow K equals 10
H e r e comma space K thin space i s space t h e space n u m b e r space o f space g i r l s space a d d e d. space
S o comma space 10 space n u m b e r space o f space g i r l s space s h o u l d space b e space a d d e d space t o space m a k e space t h e space r a t i o space 3 colon 2
K i n d l y space c h e c k space w i t h space y o u r space c a l c u l a t i o n s. space Y o u space m i g h t space h a v e space d o n e space s o m e space
c a l c u l a t i o n space e r r o r.
end style

Answered by satyajit samal | 13th Jun, 2016, 09:06: AM