1.If ( 2a + 7) / (3a + 5) = 15/17, then a = ?
a) 4
b) 2
c) 6
d) 5
2.Vivek is twice as old as his sister.five years ago his age was three times his sister's age. Find the present age of Vivek.
a) 10
b) 20
c) 30
d) 35
3.The ages of Ram and Rahim are in the ratio 7 : 5. Five years from now the ratio of their ages will be 4 : 3. Find the present age of Rahim.
a) 35
b) 30
c) 25
d) 20
4.Sum of three consecutive integers is 51. The middle one is
a) 15
b) 17
c) 14
d) 16
5.If 5a - 2 (2a -7) = 2 (3a - 1) + 7/2, then a =?
a) 3/2
b) 1/2
c) 5/2
d) 7/2
Answers
Step-by-step explanation:
1. ( 2a + 7) / (3a + 5) = 15/17
=> 2a+7 = 15 & 3a+5=17
=> 2a = 15-7 & 3a = 17-5
=> 2a = 8 & 3a = 12
=> a = 4 (option a)
from the given options a)4 is the answer
2. let present age of viveks sister = x
=> present age of vivek = 2x
given, 2x-5 = 3(x-5)
=> 2x-5 = 3x-15
=> 3x-2x = 15-5
=> x = 10
=> present age of vivek = 2x = 2(10) = 20 (option b)
3. age of Ram to Rahim = 7 : 5
let x be the proportion,
Ram and Rahims present age will be 7x and 5x resply.,
after 5 years age of Ram to Rahim is given as 4 : 3
ie., 7x-5 : 5x-5 = 4:3
=> (7x-5) / (5x-5) = 4/3
=> 3(7x-5) = 4(5x-5)
=> 21x-15 = 20x-20
=> 21x-20x = -20+15
=> x = -5
=> Rahims present age will be 5x = 5(5) = 25 (option c)
4. given, Sum of three consecutive integers is 51
let x be the middle number
=> (x-1) + x + (x+1) = 51
=> 3x = 51
=> x = 51/3
=> x = 17 (option b)
5. 5a - 2 (2a -7) = 2 (3a - 1) + 7/2
5a - 4a+14 = 6a-2 + 7/2
a+14 = 6a + (-4+7)/2
a+14 = 6a + 3/2
6a - a = 14- (3/2)
5a = (28-3)/2
a = (25/2)*(1/5)
a = 5/2 (option c)
Step-by-step explanation:
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