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.
