Aptitude Ratio And ProportionPage 2
9.  The ratio of earning to expenditure of A is 5 : 3 and that of B is 7 : 6, If the savings of A is double the that of be then what could be the ratio of total earnings of A and B together to the total expenditure of A and B together?  (a)4 : 3  (b)3 : 5  (c)5 : 3  (d)2 : 1 

Answer is: ALet the earning of A be 5x, then the expenditure of B will be 3x
So, saving of A = 5x  3x = 2x
Let earnings of B be 7y,then the expenditure of B will be 6y.
So, Saving of B = 7y6y = y
Given saving of A is double them that of B
So, 2x = 2(y)
x = y
So, The ratio of total earning A and B to the total expenditure of A and B = (5x +7y)/(3x + 6y) = (5x+7x)/(3x+6x) = 12/9 = 4:3
10.  The mean proportion between two numbers is 12. The third proportion of the same numbers is 96. Find the greater of the two numbers?  (a)12  (b)18  (c)24  (d)36 

Answer is: CLet the two numbers be a and b where a is b
âˆ´ a, b, br, 96 are in continued proposition (or geometric progression with common ratio r).
Relating the two known terms, 12 and 96, we can see that
12 (r^{3}) = 96
r = 2.
11.  Find a : b : c, given 3a + 2b = 7c and b = a + c  (a)3 : 8 : 5  (b)1 : 6 : 5  (c)1 : 2 : 1  (d)3 : 10 : 7 

Answer is: Csubstituting b with a + c in the equation 3a+2b = 7c and simplifying
we get a = c
substituting a = c in one of the two equations
b = 2c
12.  Anita divided some chocolates among her three sons such that for every 4 chocolates that the eldest son got, her second 3 chocolates. For every 2 chocolates that her second son got, her third son got 3 chocolates. If her second son 12 chocolates. Find the total number of chocolates received by the either two sons?  (a)18  (b)34  (c)46  (d)51 

Answer is: BLet the number of chocolates received by Anitaâ€™s first,
Second and third sons be a, b and c respectively.
As a/b= 4/3 , b must be multiple of 3.
As b/c= 2/3 , b must be multiple of 2
Hence b must be multiple of both 3 and 2 i.e. 6
If b = 6, a = 8 and c = 9
Hence a:b:c = 8:6:9
Total numbers of chocolates received by the other two sons = (9+8)/6 (12) = 34
13.  When Ganesh was asked about his score in last classroom test in which the maximum marks were 50, he replied , The ratio of 15 less than my score to 15 more than three times my score is 1:5. What is his score?  (a)35  (b)40  (c)45  (d)50 

Answer is: CLets, Ganesh's score be X.
so, (X 15)/(3X +15) = 1/5
5X  75 = 3X + 15
2X = 90
X = 45
14.  Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by â‚¹ 4000, the new ratio becomes 40:57. What is sumit's present salary?  (a)17000  (b)20000  (c)25500  (d)38000 

Answer is: Dthen, (2X+4000 )/( 3X+4000) = 40/57
57(2X+4000) = 40(3X+4000)
6X = 68000
3X = 34000
So, Sumit's present salary = (3X+4000) = Rs. (34000+4000) = 38000
15.  If 40% of a number is equal two third of another number, What is the ratio of first number to the second number?  (a)2:5  (b)3:7  (c)5:3  (d)7:3 

Answer is: CLet, 40% of A = 2/3 B.
then, 40/100 A = 2/3 B
A/B = 2/3 x 5/2
A/B = 5/3
So, A : B = 5 : 3
16.  If a : b = 4 : 5 and b : c = 4 : 7, Find a : b : c ?  (a)22:55:63  (b)28:36:23  (c)45:25:23  (d)20:36:63 

Answer is: DLet a:b = 5:9 and b:c = 4:7 = (4 x 9/4) : (7 x 9/4) = 9:63/4
A:b:c = 5:9:63/4 = 20:36:63
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