Answer:
Numbers are 1050, 1200, 2550, 5100.
Step-by-step explanation:
Let the four numbers are a, b, c, d.
Since second exceeds the first by 1/7 of the first.
b = a + (a/7) = 8a/7
Third exceeds the sum of first two by 200.
c = a + b + 300 = a + (8a/7) + 300 = (15a/7) + 300
Fourth exceeds the sum of the first three by 300
d = a + b + c + 300 = a + (8a/7) + (15a/7) + 300 + 300 = a + (23a/7) + 600
d = (30a/7)+600
And sum of four numbers is 9900
a + b + c + d = 9900--------(1)
By putting the values of b, c, d in the equation (1)
a + (8a/7) + (15a/7) + 300 + (30a/7) + 600 = 9900
a + (8a/7) + (15a/7) + (30a/7) = 9900 - 300 - 600 = 9000
a + [(8a + 15a + 30a)/7] = 9000
a + (53a/7) = 9000
60a/7 = 9000
a = 9000×7/60 = 1050
Now we put the values of a and get the numbers
b = 8a/7 = 8×1050/7 = 8×150 = 1200
c = (15a/7) + 300 = (15×1050)/7 + 300 = 15×150 + 300 = 2250 + 300 = 2550
and finally from equation 1
1050 + 1200 + 2550 + d = 9900
d + 4800 = 9900
d = 9900 - 4800 = 5100
Therefore the numbers are 1050, 1200, 2550 & 5100.
