Monday, July 18, 2016

1. A pipe can empty a tank in 40 minutes. A second pipe with diameter twice much as that of the first is also attached with the tank to empty it. The two together can empty the tank in:
(a)8.5 minutes   
(b)13.33 minutes
(c)30 minutes   
(d)8 minutes
(e)None of these 

1. (d) 
Here volume of water emptied by the second pipe will be 4 times to that of first 
Hence, Time take will be 1/4 of the first pipe. 
When both the pipes are open the part of the tank emptied in 1 minute
= 1/40 + 1/10 = 1/8 
Hence the tank will be emptied in 8 minutes.

2. A can do 1/2 of a piece of work in 5 days. B can do 3/5 of the same work in 9 days and C can do 2/3 of that work in 8 days. In how many days can three of them together do the work?
(a)3    
(b)5
(c)4.5  
(d)4
(e)None of these 

2. (d) 
(A+B+C) one day’s work =1/10+ 1/15+1/12= 1/4
Hence together they complete the work in 4 days

3. If the marked price of 30 articles is equal to selling price of 40 articles, then find the % discount?
(a)25%   
(b)33.33%
(c)75%   
(d) 20%
(e)None of these 

3. (a) 
MP of 30 = SP 40
MP/SP = 40/30
Discount = (10/40) * 100= 25%

4. The length of one side of a rhombus is 6.5 cm and its altitude is 10 cm. If the length of its one diagonal is 26 cm, the length of the other diagonal will be:
(a)5 cm   
(b)6.5 cm
(c)10 cm    
(d)26 cm
(e)None of these 

4. (a)  
Area =base * height =6.5*10 = 65cm2
Let the diagonal of rhombus be d1 and d2.
Area = 1/2 d1d2 = 65
= ½* 26* d2 = 65
d2 = 5

5. The average age of 30 boys in a class is 15 Years. One boy, aged 20 years, left the class, but two new boys come in his place whose ages differ by 5 years. If the average age of all the boys now in the class becomes 15 years, the age of the younger new comer is:
(a)20 year    
(b)15 year
(c)40 year    
(d)8 year
(e)None of these 

5. (b) 
Let the age of younger one be x and other is x+5
 so, x+(x+5) = (31*15)-(30*15-20)=35 
x= 15

6. The areas of two similar triangles are 81 cm2 and 49 cm2 respectively. The ratio of their corresponding heights is:
(a)9 : 7    
(b)7 : 3
(c)3 : 7    
(d)81 :49
(e)None of these 

6. (a)
h1/h2=b1/b2
1/2*b1*h1∶1/2*b2*h2 = 81 : 49
h1^2 ∶h2^2=81∶49
h1 : h2 = 9 : 7

7. If a : b = 2 : 3 and b : c = 4 : 5, find a^2 : b^2 : c^2 ?
(a)4 : 9 : 45   
(b)16 : 36 : 45
(c)16 : 36 : 20  
(d)4 : 36 : 40
(e)None of these 

7. (e) 
a:b:c = 8:12:15
a^2: b^2 :c^2: =64:144:225

8. A dealer offer a discount of 10% on the marked price of an article and still makes a profit of 20%. If its marked price is Rs. 800, then the cost price of the article is:
(a)Rs.900    
(b)Rs.800
(c)Rs.700    
(d)Rs.600
(e)None of these 

8. (d)
SP = 800 * 90/100 = 720
CP = 720 * 100/120 = 600

9. The capacities of two hemispherical vessels are 6.4 litres and 21.6 litres. The ratio of their inner radii is
(a) 4 : 9  
(b) 16 : 81
(c) √2:√3  
(d) 2 : 3
(e) None of these 

9. (d)
r13 : r23 = 6.4 : 21.6
r1 : r2 = 4 : 6 = 2 : 3

10. Pipe A alone can fill a tank in 8 hours. Pipe B alone can fill it in 6 hours. If both the pipes are opened and after 2 hours, pipe A is closed, then the other pipe will fill the tank in
(a) 6 hours  
(b) 3.5 hours
(c) 4 hours  
(d) 2.5 hours
(e) None of these 

10. (d)
If both pipes are open,
1/8+1/6=7/24
For 2 hours = 2 * 7/24 = 7/12 tank is filled
Remaining empty tank = 1- 7/12 = 5/12

Therefore, B can fill the remaining tank in 5/12 * 6 = 2.5 hours

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