Sample Material of Online Coaching For SSC CGL (Tier - 2) - Unitary Method
Sample Material SSC CGL TIER-2 Online Coaching
Numerical Aptitude (Chapter: Unitary Method)
Unitary method is the basic area of arithmetic.
Direct Proportion
Two quantities are said to be directly proportional, if on
the increase in one the other increases proportionally or on the decrease in one
the other decreases proportionally.
eg, More the numbers of articles, More is the cost.
More the number of workers, More is the work done.
Less the number of articles, Less is the cost.
Less the number of workers, Less is the work done.
Indirect Proportion
Two quantities are said to be indirectly proportional, if on
the increase in one the other decreases proportionally or on the decrease in one
the other increases proportionally.
eg, More the number of workers, less is the number of days required to finish a
work. More the speed, less is the time taken to cover a certain distance.
Less the number of workers, more is the number of days required to finish a
work. Less the speed, more is the time taken to cover a certain distance.
Chain Rule
When a series of variables are connected with one another, that we know how much of the first kind is equivalent to a given quantity of second, how much of the second is equivalent to a given quantity of the third and so on. The rule by which we can find how much of the last kind is equivalent to a given quantity of the first kind is called the Chain Rule.
Example 1: If 12 apples cost – 216, what is the cost of 3 dozen apples ? Solution. Let the required cost be Rs x. Also, 3 dozen apples = 35 apples more apples, more cost (Direct Proportion); Apples Cost in – 12 216 36 x 12 × x = 36 × 216 Þ x = = – 648
Example 2: A contractor undertakes to complete a road 420 m long in 140 days and employ men for the work. After 70 days he finds that only 140 m of the road is made. How many men should the contractor employ more so that the work may be completed in time? Solution. In the second case in (140–70) days ie, 70 days the length of the road to be construct (420-140) m ie, 280 m. Let the number of men employed be x. More length of road, More men (Direct Proportion) Days Length of road in metre Men 70 140 28 70 280 x x=(280/140)x28 = 56 men Additional men required= 56 – 28 = 28 men
:: Home Assignment for Practice ::
1. Cost of 24 pens is Rs 96. Find the cost of 16 such pens.
(a) Rs 66
(b) Rs 64
(c) Rs 62
(d) Rs 68
2. A bus travels 240 km in 3 h. How long will it take to travel 360 km?
(a) 5 h.
(b) 4 h
(c)9/2 h
(d)11/2 h
3. The temperature dropped 18°C in the last 24 days. If the rate of temperature drop remains constant, then how many degrees will the temperature drop in the next 32 days?
(a)49°/2
(b)22° C
(c)45°/2
(d) 24° C
4. Cost of 8 dozen bananas is Rs 180. How many bananas can be purchased for Rs 30?
(a) 16 bananas
(b) 24 bananas
(c) 14 bananas
(d) 22 bananas
5. A man pays Rs 13000 as rent for 4 months. How much does he pay for the whole year, if rent per month remains the same?
(a) Rs 48000
(b) Rs 39000
(c) Rs 46000
(d) Rs 47000