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A sum of Rs. 4,360 was to be divided among A, B, C and D in the ratio 3 ∶ 4 ∶ 5 ∶ 8, but it was divided in the ratio \(\dfrac{1}{3} : \dfrac{1}{4} : \dfrac{1}{5} : \dfrac{1}{8}\) by mistake. Which of the following statements will hold true as a result? 1. B received Rs. 318 less2. D received Rs. 1,144 more3. A received Rs. 9564. C received Rs. 130 less |
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Answer» Correct Answer - Option 4 : C received Rs. 130 less Given: Total sum = Rs. 4360 Ratio of A, B, C and D = 3 ∶ 4 ∶ 5 ∶ 8 By mistake taken ratio of A, B, C and D = (1/3) ∶ (1/4) ∶ (1/5) ∶ (1/8) Concept Used: Ratio method used here. Calculation: Let amount divided among A, B, C and D be 3x, 4x, 5x and 8x. According to the question, 3x + 4x + 5x + 8x = 4360 ⇒ 20x = 4360 ⇒ x = 218 Amount A got = 3x = 3 × 218 = 654 Amount B got = 4x = 4 × 218 = 872 Amount C got = 5x = 5 × 218 = 1090 Amount D got = 8x = 8 × 218 = 1744 In the given question ratio taken wrong So, new ratio = (1/3) ∶ (1/4) ∶ (1/5) ∶ (1/8) To change fraction ratio into simple ratio by taking LCM of denominator LCM of 3, 4, 5 and 8 is is 120. New ratio = [(1/3) × 120] ∶ [(1/4) × 120] ∶ [(1/5) × 120] ∶ [(1/8) × 120] ⇒ Required ratio = 40 ∶ 30 ∶ 24 ∶ 15 Let the mistake ratio be 40y, 30y, 24y and 15y. 40y + 30y + 24y + 15y = 4360 ⇒ 109y = 4360 ⇒ y = 40 New amount A received = 40y = 40 × 40 = 1600 New amount B received = 30y = 30 × 40 = 1200 New amount C received = 24y = 24 × 40 = 960 New amount D received = 15y = 15 × 40 = 600 So, C got = 1090 – 960 = 130 ∴ Option D is right C has 130 less. |
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