Question

a bonus of 9 lakh is divided among 110 supervisors and workers in the ration 5:4 if the individual shares of supervisors and workers were in the ration 3:2.what is the number of supervisors

Answer 1

Answer:

Required number of supervisors is 50.

Step-by-step explanation:

It is given that the total amount of bonus is Rs 9,00,000 ( 9 lacks ), which is divided among 110 supervisors and few workers.

Let the number of supervisors be a and the number of workers be b and, bonus of one worker and one supervisor be Rs b and Rs c respectively.

= > Number of supervisors + Number of workers = 110

= > a + b = 110

= > a = 110 - b       ...( 1 )

According to the situation :

= > Total amount of bonus = Bonus of supervisors + Bonus of workers

= > Rs 900000 = ( Number of supervisors x bonus of one supervisor ) + ( Number of workers x bonus of one worker )

= > Rs 900000 = ( a x Rs c ) + ( b x Rs d )

= > 900000 = ac + bd

{ Now, bonus of supervisors is ac and bonus of workers is bd, where a is the number of workers }.

Given, bonus of 9 lakh is divided among 110 supervisors and workers in the ratio 5:4.

It means : -

= > ( Bonus of supervisors ) : ( bonus of workers ) = 5 : 4

= > ( Rs ac ) : ( Rs bd ) = 5 : 4

= > ac : bd = 5 : 4

= > ac / bd = 5 / 4               ...( i )

Also, given, the individual shares of supervisors and workers were in the ration 3:2.

It means : -

= > ( Bonus of one supervisor ) : ( bonus of one worker ) = 3 : 2

= > Rs c : Rs d = 3 : 2

= > c  : d = 3 : 2

= > c / d = 3 / 2            ...( ii )

Substituting the values of c / b from ( ii ) in ( i ) : -

= > ac / bd = 5 / 4

= > a / b x c / d = 5 / 4

= > a / b x 3 / 2 = 5 / 4               [ c / d = 3 / 2  ]

= > a / b = 5 / 4 x 2 / 3

= > a / b = 5 / 6

= > a / ( 110 - a ) = 5 / 6        { from ( 1 ) }

= > 6a = 5( 110 - a )

= > 6a = 550 - 5a

= > 6a + 5a = 550

= > 11a = 550

= > a = 550 / 11

= > a = 50

Hence the required number of supervisors is 50.