Six more than one fourth of a number is 2/5 of the number. Find the number
Answers
Step-by-step explanation:
Given :-
6 more than one fourth of a number is 2/5 of the number.
To find :-
Find the number ?
Solution :-
Let the given number be X
One fourth of the number
=> (1/4)×X
=> (1×X)/4
=> X/4
6 more than one fourth of the number
= (X/4)+6
And
2/5 th of the number
=> (2/5) of X
=> (2/5)×X
=> (2×X)/5
=> 2X/5
According to the given problem
6 more than 1/4 of the number = 2/5 th of the number
=> (X/4)+6 = 2X/5
=> 6 = (2X/5)-(X/4)
LCM of 5 and 4 = 20
=> 6 = [(2X×4)-(X×5)]/20
=> 6 = (8X-5X)/20
=> 6 = 3X/20
=> 3X/20 = 6
=> 3X = 6×20
=> 3X = 120
=> X = 120/3
=> X = 40
Therefore, X = 40
Answer:-
The required number for the given problem is 40
Check:-
The number = 40
6 more than 1/4 of the number
=> (1/4)×40 + 6
=> (40/4)+6
=> 10+6
=> 16 -------(1)
and
2/5 th of the number
=> (2/5)×40
=> (2×40)/5
=> 2×8
=> 16 ------(2)
From (1)&(2)
6 more than 1/4 of the number = 2/5 th of the number
Verified the given relations in the given problem.