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

Solution: 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 × 7 : 13 × 7 = 112 : 91 ⇒ a + b + c : a + c = 14 : 9 = 14 × 8 : 9 × 8 = 112 : 72 So, 112x = 1904 ⇒ x = 1904/112 = 17 Now, b + c = 91 × 17 = 1547 ⇒ a + c = 72 × 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 a/(b + c) + 1 = (3/13) +1 a+ b + c /(b + c) = 16/13 1904/(b + c) = 16/13 b+ c = 1547 (i) similarly, b ∶ (a + c) = 5 ∶ 9 a+ b + c /(a + c) = 14/9 1904/(a + c) = 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.