Question

If a + b + c = 1904, a ∶ (b + c) = 3 ∶ 13 and b ∶ (a + c) = 5 ∶ 9, then what will be the value of c?

• A. 776
• B. 879
• C. 867
• D. 680

Answer 1

Answer:

C. 867

Given : 

a + b + c = 1904

a ∶ (b + c) = 3 ∶ 13

b ∶ (a + c) = 5 ∶ 9

Calculation : 

⇒ a ∶ (b + c) = 3 ∶ 13   --------------(1)

⇒ b  ∶ (a + c) = 5 ∶ 9     ------------------(2)

By adding one on both LHS and RHS of both the equations,

⇒ a + b + c : b + c = 16 : 13

⇒ a + b + c : a + c = 14 : 9 

Now making (a : b : c) same we get

⇒ a + b + c : b + c = 16 : 13 $=16\times{7}$ : $13\times{7}$ = 112 :  91

⇒ a + b + c : a + c = 14 : 9 = $14\times{8}$ : $9\times{8}$ = 112 : 72

So, 112x = 1904

$⇒x=\frac{1904}{112}=17$

$Now,b + c=91\times{17}=1547$

⇒ a + c = $72\times{17}$ = 1224

Now a + b + c = 1904

⇒ a + 1547 = 1904, a = 357

⇒ b + 1224 = 1904, b = 680

Now 357 + 680 + c = 1904

⇒ c = 1904 - 357 - 680 = 867

∴ The correct answer is 867.

Alternate Method 

a + b + c = 1904

a ∶ (b + c) = 3 ∶ 13

$\frac{a}{(b + c)}+1=\frac{3}{13}+1$

$\frac{a+b+c}{(b+c)}=\frac{16}{13}$

  

$\frac{1904}{(b+c)}=\frac{16}{13}$

 

b+ c = 1547  (i)

similarly,

b ∶ (a + c) = 5 ∶ 9

$\frac{a+b+c}{(a+c)}=\frac{14}{9}$

     

$\frac{1904}{(a+c)}=\frac{14}{9}$

 

a+ c = 1224  (ii)

adding Equation (i) & (ii)

a + b + c + c = 1547 +1224

1904 + c = 2771

c = 867

∴ The correct answer is 867.