Problems Based on Fraction

A man earns ₹ 7,500 per month. If he saves `1/4` of his earnings, find:
(a) his savings per month (b) his expenditure per month. 

Solution:
(a) Savings per month = `1/4` of his earnings

                                     = `1/4` of ₹ 7,500

                                     = ₹ `1/4` ×  7,500

                                      = ₹ 1,875 
(b) His expenditure per month = ₹ 7,500 − ₹ 1,875
                                                  = ₹ 5,625 
Alternative method:
In fractions, the whole quantity is considered to be 1. 
Since the man saves `1/4` of his earnings,
his expenditure = 1 −  `1/4`

                          = `"4 - 1"/4`

                          =  `3/4` of his earnings
⇒ Expenditure per month
                          =  `3/4` × ₹ 7,500

                          = ₹5,625

There are 12 dozen bananas in a basket. `5/24` of them are rotten and `1/3` of them get eaten. How many bananas are left? 
Solution:
Total number of bananas = 12 dozen = 12 × 12 = 144

No. of rotten bananas = `5/24` of 144 =  `5/24` × 144 = 30

No. of bananas eaten =  `1/3` of 144 = `1/3` × 144 = 48

Since 30 + 48 = 78

∴ No. of bananas left = 144 - 78 = 66

A man spends `2/5` of his money and is left with ₹30. How much did he initially have?

Solution:
Remember, when solving problems involving fractions, the whole quantity is always considered to be 1.

Since the man spends `2/5` of his money

Therefore, Money left with him = (1 − `2/5`) of his money = `3/5` of his money

Given: `3/5`of his initial money =  ₹30

∴ Initially he had ₹30 × `5/3` =  ₹50

After travelling 10 km, Dev found that `1/3` of his journey was still left. How long was his total journey? 

Solution:
Since `1/3` of the journey is left,

therefore, 1 −  `1/4` = `2/3` of the journey is completed.

Given:  `2/3` of the total journey = 10 km

∴ Total journey = 10 km × `3/2` =  15 km