Percentage Concept of BY and TO - problems

Percentage Concept of BY and TO - problems

Due to fall in manpower, the production in the factory decreases by 60% by what per cent should the working hour be increased to restore the original production in the factory? 

Solution:

Manpower x working hours = production

  (-60%) = 3/5 -------> 3/2 = (+150%)                        (3/5 -->  3/5-3  = 3/2)

hence by 150% working hours will be increased. It means the new working hours will be 2.5 times (not 1.5 times) of the original time.


Two numbers are respectively 25% and 40% less than a third number. What per cent is the second of the first?

Solution:

consider A,B,C three numbers and assume C = 100 ( as a base)

A                 B                    C
75                60 <-----------100
                             (-40%)

<------------(-25%)------------

Now  60/75 x100 = 80%


A person gives 10% to his wife 10% of the remaining to a hospital (as a donation) again 10% of the remaining to prime minister's relief fund. Then he has only 7290rs. with him. What was the initial sum of money with that person?

Solution:

Since he gives 10% so he is left with 90% of the original sum and since he does the same with the remaining (or left) amount. so it forms a chain.

therefore remaining amount = (x) x 0.9 x 0.9 x 0.9
                                             = 0.729x = 7290

=> x = 10,000, where x is supposed to be initial amount.

Initially a shopkeeper had n chocolates. A customer bought 10% chocolate from n then another customer bought 20% of the remaining chocolates, after that one more customer purchased 25% of the remaining chocolates. Finally shopkeeper is left with 270 chocolates in his shop. How many chocolates were there initially in his shop?

Solution:

n x 0.9 x 0.8 x 0.75 = 270

n = 270 x 10,000 / 9 x 8 x 75

n =500