There are some sweets and chocolates in a jar. If 75 sweets are removed from the jar, the total number of sweets and chocolates left will be 6 times the number of sweets left. If 60 chocolates are removed from the jar, the total number of sweets and chocolates left will be 3 times the number of sweets left. What is the total number if sweets and chocolates in a jar?
Let, there are x sweets and y chocolates in the jar.
When 75 sweets are removed,
there are (x - 75) sweets.
According to the given
Condition,
x - 75 + y = 6 (x - 75)
or, x + y - 75 = 6x - 450
or, 6x - x - y + 75 - 450 = 0
or, 5x - y - 375 = 0
or, 5x - y - 375 —- (i)
when 60 chocolates are
removed from the jar,
then there are (y - 60)
chocolates.
According to the given
problem,
x + y - 60 = 3x
or, 3x - x - y + 60 = 0
or, 2x - y = - 60 —- (ii)
Now, (i) - (ii) gives,
5x - y - 2x + y = 375 - (- 60)
or, 3x = 75 + 60
or, 3x = 435
or, x = 435/3 = 145
from (ii),
(2 * 145) - y = - 60
or, 290 - y = - 60
or, y = 290 + 60 = 350
Total no. of, sweets is 145 and chocolates is 350