Question

Find in what ratio the total wages of the workers of a factory be increased or decreased,if there be a reduction in the number of workers in the ratio 15:11 and an increment in their wages in the ratio 22:25.

Answer 1

hello,
we have that:
r(reduction in wage) = 15/11;
i(increment in wage )= 22/25

we calculate the total wages ratio:
t=r×i;
=(15/11)×(22/25);
=6/5

So, total wages ratio = 6/5

bye :-)

Answer 2

SOLUTION:-

Let us assume,

x  =  No. of workers,    y  =  Average wages per worker

Then, total wages = (no. of workers) x (wages per worker)

Total wages   =   xy  or  1xy --------- (1)

After reduction in workers in the ratio 15 : 11,

no. of workers  =  11x / 15

After increment  in wages in the ratio 22 : 25,

wages per worker  =  25y / 22

Now, the total wages is

=  (11x / 15) ⋅ (25y / 15)

=  5xy / 6  

So, the total wages after changes  is

=  5xy / 6  ------------ (2)

From (1) and (2) we get that the total wages get decreased from xy to 5xy/6. 

So, the decrement  ratio  is

=  xy : 5xy/6

Divide both the terms by "xy".

=  1 : 5/6

Multiply both the terms by 6.

=  6 : 5

Hence, the total wages will be decreased in the ratio  6 : 5