Question

what must be added to no. 1,3,10,18 so that they are in proportion.?

Answer 1

let the no added be k

so 1+k/3+k=10+k/18+k

so k= 2

Answer 2

1 : 3 : : 10 : 18 = 1 : 3 : : 5 : 9

number added = a

a + 1 / a + 3 = a + 5 / 9 + a

(a + 1) (a + 9) = (a + 3) (a + 5)

a^{2} + 10a + 9 = a^{2} + 8a + 15  

10a + 9 = 8a + 15

10a - 8a = 15 - 9

2a = 6

a = 6/2

a = 3

1:3 : : 5:9 = 1 +3:3 + 3: : 5 + 3:9 + 3 = 4:6 : : 8:12 = 2:3 : : 2:3

Therefore, they are in propotion.

ANSWER = 3