Model Questions on MATH SET 3

1. A certain amount was to be distributed among A, B and C in the ratio 1 : 2 : 3 respectively, but was erroneously distributed in the ratio 4 : 3 : 2 respectively. As a result of this, C got Rs. 60 less. What is the total amount?
(a) Rs. 216                                          
(b) Rs. 48            
(c) Rs. 108                                           
(d) Rs. 36  


2. Gaurav scored 83 marks in subject A. He scored 75% marks in subject B and X marks in subject C. Maximum marks in each subject were 120. The overall percentage marks obtained by Gaurav in all three subjects together were 80%. How many marks did he score in subject C?
(a) 94                                    
(b) 106                
(c) 85                                    
(d) 115    
           
3. Monika enters a shop to buy pen, pencils and erasers. She has to buy at least 7 units of each. She buys more pencils than pen and more erasers than pencils. She picks up a total of 26 items. How many pencils does she buy?
(a) 10 or 11                                        
(b) 9 or 10          
(c) 8 or 9                                              
(d) 7 or 9     

                       
4. Rs. 31,394 are divided between A and B in the ratio 5 : 6. What is the difference between thrice the share of A and twice the share of B?
(a) Rs. 6582                        
(b) Rs. 5862      
(c) Rs. 8562                        
(d) Rs. 8652        
              
5. Sum of three consecutive numbers is 2475. What is 35% of the smallest number?
(a) 251.6                                              
(b) 288.4            
(c) 308.4                                              
(d) 296.8        
                    
6. The product of three consecutive even numbers is 2688. What is five times the second number?
(a) 80                                    
(b) 100                
(c) 60                                    
(d) 70          
         
7. The sum of the ages of 4 members of a family 5 years ago was 106 years. Today when the daughter has been married off and replaced by a daughter in law, the sum of their ages is 108. Assuming that there has been no other change in the family structure and all the people are alive, what is the difference in the age of the daughter and the daughter in law?
(a) 22 years                        
(b) 11 years       
(c) 25 years                        
(d) 18 years        
               
8. When X is subtracted from the numbers 10, 14 and 20, the remainders are in continued proportion. What is the value of X?
(a) 2                       
(b) 1                     
(c) 4                       
(d) 5      
                     
9. A and B together can complete a task in 4 days. B and C together can complete the same task in 6 days. A and C together can complete the same task in 8 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of days taken by C when completing the same task alone?
(a) 5 : 3                                 
(b) 5 : 1                               
(c) 3 : 5                                 
(d) 1 : 5

10. The ratio of the present ages of Anju and Sandhya is 13:17 respectively. Four years ago the ratio of their respective ages was 11:15. What will be the respective ratio of their ages six years hence?
(1) 3:4                                         (2) 7:8                         
(3) 5:4                                         (4) 4:5



Answers:

1. (a)
Let the total amount be x.
C’s original share = 3x / 6 = x / 2
C’s new share = 2x / 9
Now
(x / 2) – (2x / 9) = 60
x = 216

2. (d)
Gaurav’s marks in A = 83
Gaurav’s marks in B = 75% of 120 = 90
Now
(83 + 90 + x) / 360 * 100 = 80
x = 115

3. (c)
No. of erasers > No of pencils > No of pens
Possible combinations
Erasers = 11, Pencils = 8, Pens = 7 
OR
Erasers = 10, Pencils = 9, Pens = 7

4. (c)
Let the shares of A and B be 5x and 6x. Now
5x + 6x = 31394
x = 2854
Required difference = (3 * 5)x – (2 * 6)x = 3x = 8562  

5. (b)
Let the numbers be x, x + 1 and x + 2. Now
x + (x + 1) + (x + 2) = 2475
x = 824
Required number = 35% of 824 = 288.4

6. (d)
Let the three numbers be x, x+2 and x+4. Now
x * (x + 2) * (x + 4) = 2688
x = 12
So the numbers are 12, 14 and 16.
Required number = 5 * 14 = 70

7. (d)
Sum of the ages of 4 members 5 years ago = 106 years
Sum of the ages at present if there was no change in family = 106 + 5 * 4 = 126
Sum of the ages after the daughter is replaced by daughter-in-law = 108
Difference in the age of the daughter and the daughter in law = 126 – 108 = 18

8. (a)
(10 – x) / (14 - x) = (14 - x) / (20 - x)
x = 2

9. (d)
Let the work to be done = 24 units
Work done by A and B in one day = 6 units
Work done by B and C in one day = 4 units
Work done by A and C in one day = 3 units
Work done by all three (A, B and C) in two days = 6 + 4 + 3 =13 units
Work done by all three (A, B and C) in one day = 13/2 = 6.5 units
Work done by A alone in one day = 6.5 – 4 = 2.5 units
Work done by C alone in one day = 6.5 – 6 = 0.5 units
Ratio of efficiencies of A and C = 2.5 : 0. 5 = 5 : 1
Ratio of time taken by them to complete the work alone = 1 : 5

10. (4)
            Let the present ages of Anju and Sandhya be 13x and 17x years 
             respectively. 
                ∴13x-4⁄17x-4 =11⁄15 
            =>187x-44=195x-60
            =>195x-187x=60-40
            =>x=2
                ∴Required ratio= (13×2+6):(17×2+6)
            =4:5