Practice questions on Unitary method

1. If cost of 24 oranges is  72, then find out the cost of 120 oranges. [Bank Clerks 2009]

Solution
Given cost of 24 oranges = 72
            Cost of 1  orange   = 72/24
                                             = 3
Therefore
       Cost of 120 oranges = 3 × 120
                                           = 360

2. If cost of 15 eggs is 75, then find out the cost of 4 dozens eggs. [Bank Clerks 2010]

Solution
Given cost of 15 eggs = 75
            Cost of 1 egg    = 75/15
                                       = 5
Therefore
     Cost of 4 dozens ( 4× 12 = 48) eggs
                                        = 5 × 48
                                        = 240

3. A worker makes a toy in every 2 h. If he works for 80 h, then how many toys will he make? [Hotel Mgmt. 2008]

Solution
Let number of toys be x
More hours, more toys (Direct proportion)
                  2 : 80 :: 1 : x
                 x = 80/2
                    = 40 toys

4. 12 men can do a piece of work in 24 days. How many days are needed to complete the work, if 8 men are engaged in the same work? [IDBI Officers 2010]

Solution
Since 12 men can do the work in 24 days
Therefore 1 man will do it in 12  × 24 days
   8 men will do it in (12 × 24) / 8 days
                                     = 36 days
 Hence required number of days  = 36 days

5. If 45 m of a uniform rod weights 171 kg, then what will be the weight of 12 m of the same rod? [MBA 2008]

Solution
Since weight of 45 m rod = 171 kg
Therefore weight of 1 m rod = 171/45 kg
Weight of 12 m rod =( 171 /45) × 12
                                    = 45.6 kg
6.  22 men can complete a job in 16 days. In how many days, will 32 men complete that job? [Bank Clerks 2009]

Solution
Since  22 men do the work in 16 days
Therefore 1 man will do the work in 16 × 22 days.
   32 men will do the job in (16 × 22)/32 days
                                                   = 11 days
Therefore required number of days = 11 days

7.If in a hostel, food is available for 45 days for 50 students. For how many days will this food be sufficient for 75 students? [CGPSC2013]

Solution
Since for 50 students, food is sufficient for 45 days
For 1 student, food is sufficient for 45 × 50 days
Therefore for 75 students, food is sufficient for (45 × 50)/75
                             = 30 days

8.In a garrison, there was food for 1000 soldiers for one month. After 10 days, 1000 more soldiers joined the garrison. How long would the soldiers be able to carry on with the remaining food? [CSAT2013]

Solution
Since for 1000 soldiers, remaining food is sufficient for
                               30 - 10 = 20 days
Therefore for 1000 + 1000 = 2000 soldiers, food will be sufficient for  (1000 / 2000) ×20 = 10 days

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