1. Two numbers are in the ratio 5:3. If they differ by
18, what are the numbers?
2. The ages of Rahul and Harroon are in the ratio 5:7
four years later, the sum of thier ages will be 56
years. What is their persentages?
3. A rational number is such that when you multiply it
by 5/2 and add 2/3 to the product, you get -7/12.
What is the number?
4. Three consecutive integers add up to 51. What are
these integers?
Answers
Answer:
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Answer:
1) Solution :-
Let us consider the ration of two numbers be x.
The two numbers are 5x and 3x
Since two numbers differ by 18, we can write the equation :-
5x – 3x = 18
2x = 18x= 9
Therefore the two numbers are
5x = 5 x 9 = 45and
3x = 3 x 9 = 27
∴ The two numbers are 45 and 27.
2) The present ages of Rahul and Haroon are 20 and 28 respectively.
Solution:
Let the Ages of Rahul and Haroon be R and H .
Given ratio :- R/ H = 5/7
=> R = 5H /7 ___(i)
Four years later the sum of their ages will be 56 yrs .
( R+4)+(H+4) = 56
=> R+H = 48 _____(ii)
By solving the equation (i) and (ii) we get
5H /7 +H = 48
=> 5H + 7H = 48 × 7
=> 12 H = 336 => H = 28
Substitute H= 28 in equation (ii)
R + 28 =48
=> R = 20
Hence , the present ages of Rahul and Haroon are 20 and 28 respectively
3) Solution :-
Let the rational number be x
ATQ ,
5/2 x +2/3 = -7/12
Transpose 2/3 to RHS
5x/2 = - 7/12 - 2/3
=> 5x/2 = -15/12
=> x = -1/2
Therefore , the rational number is -1/2 .
4) Three consecutive integers add up to 51. The three consecutive integers are 16,17 and 18 .
Solution :-
Let three consecutive integers be x , x+1 and x+2 .
Three consecutive integers add up to 51 .
ATQ ,
x+x+1+x+2 = 51
=> 3x +3 = 51
=> 3 ( x+1) = 51
=> x+1 = 51/3 = 17
=> x =17 -1 =16
Therefore , the numbers are :-
x = 16
x +1 = 16 + 1 =17
x +2 = 16 +2 = 18
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