Direction : Study the following questions carefully and choose the right answer.
Important for :
1
A sum of Rs. 3,240 was fixed to complete a work. 54 workers completed the work in 8 days and the sum was divided equally among the workers. If the work was to be completed in 3 days then how much less money each worker would receive compared to when the work was completed in 8 days (sum is divided equally among the workers)? 
» Explain it
B
Total number of workers need to complete the work in 3 days = M1D1 = M2D2

Let the number of workers = x

then 54 × 8 = X × 3, x = 18 × 8 = 144

Each worker will receive = 

  3240  = 22.5
144

In the first case when the work was completed in 8 days each worker received

3240  = 60
54

Required difference = Rs. 37.5

Hence, option B is correct.

2
If an article was sold at 18% profit on cost price then the selling price of the article was Rs. 9381. What would have been the selling price of the article if it was sold at 25% profit?
» Explain it
A
Let the CP of the article = x

Then 18% profit on x = (100 + 18)% of x = 9381

X =  9381 × 100  =
118

79.5 × 100 = 7950 = cp
 
When article was sold at 25% profit then CP = 125% of 7950 = 9937.5

Hence, option A is correct.
 
3
In a mixture of milk and water, the concentration of milk becomes 40% if one litre of water is added in that mixture. After adding another one litre water, the concentration of milk becomes 33.33%. find the concentration of milk in the original mixture?
» Explain it
A
Let the quantity of milk in the original mixture = x litres

And the quantity of water = y litres

The total quantity of mixture = x + y litres

When 1 litre of water is added then the total quantity of the mixture = x + y + 1 litres

According to the question, x = quantity of milk = 40% of (x + y + 1)

3x = 2y + 2 .... (i)

After adding another 1 litre of water, the quantity of mixture = x + y + 1 + 1 = x + y + 2 litres

Now, according to the question, x = quantity of milk will become = 33.33% of (x + y + 2)

3x = x + y + 2

2x = y + 2 ..... (ii)

Bu solving equation (i) and equation (ii)

X = 2 and y = 2

The concentration of the milk in the mixture

2 × 100  = 50%
4

Hence, option A is correct.

4
If the difference between the compound interest and simple interest on a sum of money for 2 years at 4% per annum is Rs. 39.68 then find the sum of simple interest and compound interest for two years on the same sum of money and at the same rate of the interest?
» Explain it
B
Let the principal = x

SI = X × 2 ×  4
100

CI = X  ( 1 +  4 ) 2  – X
100  

CI – SI =  [ X ( 1 +  4 ) 2
100  

 – X ]  – X × 2 ×  4
100

By solving, x = 24800

CI + SI = 

[ 24800  ( 1 +  4 ) 2  – 24800  ]  –
100  

 24800 × 2 ×  4
100

By solving, CI + SI = 4007.68

Hence, option B is correct.
 
5
Ratio of speed of boat in still water to speed of stream 8 : 1. 67.5 km is travelled downstream in 2.5 hours. Difference between speed of boat in still water and speed of stream?
» Explain it
C
Downstream speed of boat

67.5  km/hr = 27 km/hr
2.5

Ratio of speed of boat in still water to speed of stream = 8 : 1

So, 9 units = 27 km/hr

1 unit = 3 km/hr

∴ Difference between speed of boat in still water and speed of stream = (8 – 1) = 7 units

= 7 × 3 = 21 km/hr.

Hence, option C is correct.