The sum of two number is 4000. If 15% of one number is equal to 25% of the other. Find both numbers.
a) 1000, 3000
b) 2400, 1600
c) 2500, 1500
d) 1200, 2800
Answers
Answer:
c) 2500, 1500
Step-by-step explanation:
let the 2 given nos. be 'x' and 'y' respectively
according to first condition
x + y = 4000 ......( 1 )
according to second condition
15x / 100 = 25y / 100
= 15x = 25y ..... as hundreds gets cancelled
= 3x = 5y ...... after simplification
= 3x - 5y = 0 ......( 2 )
comparing both the equations
x + y = 4000
3x - 5y = 0
Multiplying equation ( 1 ) by 5
= 5x + 5y = 20000 ......( 3 )
comparing equation ( 2 ) and ( 3 )
= 5x + 5y = 20000
= 3x - 5y = 0
adding equation ( 2 ) and ( 3 )
= 5x + 5y = 20000
= 3x - 5y = 0
----------------------------
= 8x = 20000
x = 20000 / 8
x = 2500
putting x = 2500 in equation ( 1 )
x + y = 4000
2500 + y = 4000
y = 4000 - 2500
y = 1500
therefore x = 2500 & y = 1500
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Answer
Let x and y be the two numbers.
First equation:
x+y=4000
Second equation (remember 15% of a number means .15 times the number):
.15x=.25y
Isolate y in the first equation:
x+y=4000
y=4000−x
Substitute this into the second equation:
.15x=.25(4000−x)
Distribute and solve for x:
.15x=1000−.25x
.4x=1000
x=2500
Substitute this into first equation written in terms of y:
y=4000−x
y=4000−(2500)
y=1500