If (a+b):c=11:9 and (b+c):a=5:3, then find a:b:c ​

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19 Apr 2022 Ratio & Proportion

If (a+b):c=11:9 and (b+c):a=5:3, then find a:b:c ​

OPtion

1) 5 : 6 : 18
2) 6 : 7 : 9
3) 15 : 7 : 9
4) 5 : 7 : 18
5) 15 : 6 : 18
6) 10 : 7 : 18
7) 12 : 7 : 9
8) 15 : 7 : 18
9) 10 : 12 : 9
10) None of these

Solution

(a+b)/c = 11/9 ⇒ 9a + 9b = 11c ---(i)
(b+c)/a = 5/3 ⇒ 3b + 3c = 5a ---(ii)
Multiplying Eqn (ii) by 3, 9b + 9c = 15a ---(iii)
Now subtracting Eqn. (i) from (iii), we get 9c - 9a = 15a - 11c
20c = 24a or a/c = 5/6
As (a+b)/c = 11/9 ⇒ a/c + b/c = 11/9
5/6 + b/c = 11/9
⇒ b/c = 7/18
We have a:c = 5:6 and b:c = 7:18.
a : b : c = (5x3) : 7 : 18 = 15 : 7 : 18

Correct Option: 8 Best Solution (2)

G.S.Kantharao   2 years AGO

(a+b):c=11:9,(b+c):a=5:3
9a+9b=11c,3b+3c=5a
9b+9c=15a
9a-9c=11c-15a
24a=20c=>a:c=5:6
Now (a+b)/c=11/9
A/c+b/c=11/9
b:c=11/9-5/6=7/18
A:c=5:6
b:c=7:18
A:b:c=15:7:18
So my option is 8👈

Like? Yes (5) | No   

Varun   2 years AGO

Solving linear equation 3b+3c=5a
And 11c=9a+9b
We get a:c = 5:6
And b:c = 7:18
Making c same
a:b:c = 15:7:18

Like? Yes (1) | No