3. Two numbers are in the ratio 3 : 5. If 7 is added to each one, then the ratio becomes 11 : 16. Find the numbers. (give correct answer with explanation)
Answers
Answer:
15 and 25
Step-by-step explanation:
Note: if two numbers are in ratio say k:a
Then the two numbers are kx and ax where x is positive integer
Sol: let the numbers be 3x and 5x
According to given
=> (3x + 7):(5x + 7) = 11:16
=> 11(5x + 7) = 16(3x + 7)
=> 55x + 77 = 48x + 112
=> 7x = 35
=> x = 5
Numbers are (3 × 5) and (5 × 5)
15 and 25
Step-by-step explanation:
Given :-
Two numbers are in the ratio 3 : 5. If 7 is added to each one, then the ratio becomes 11 : 16.
To find :-
The numbers.
Solution :-
Given that
The ratio of two numbers = 3:5
Let they be 3X and 5X
If 7 is added to 3X then it will be 3X+7
If 7 is added to 5X then it will be 5X+7
The new ratio of the numbers = (3X+7):(5X+7)
According to the given problem
The new ratio = 11:16
Therefore, (3X+7):(5X+7) = 11:16
=> (3X+7)/(5X+7) = 11/16
On applying cross multiplication then
=> 11(5X+7) = 16(3X+7)
=> 55X+77 = 48X+112
=> 55X-48X = 112-77
=> 7X = 35
=> X = 35/7
=> X = 5
Therefore, X = 5
If X = 5 then 3X = 3(5) = 15
If X = 5 then 5X = 5(5) = 25
The two numbers = 15 and 25
Answer:-
The required two numbers are 15 and 25
Check :-
The two numbers = 15 and 25
Their ratio = 15:25
= 15/25
= (3×5)/(5×5)
= 3/5
= 3:5
and
If 7 is added to 15 and 25 then they becomes
15+7 = 22 and 25+7 = 32
The ratio of new numbers = 22:32
= 22/32
= (2×11)/(2×16)
= 11/16
= 11:16
Hence, Verified the given relations in the given problem.
Used formulae:-
→ a:b can be written as a/b