Ratio, Proportion
- If x : y = 3 : 1, then x3 – y3 : x3 + y3 = ?
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x = 3 ⇒ x3 = 27 y 1 y3 1 ⇒ x3 − y3 = 27 − 1 x3 − y3 27 + 1
[By componendo and dividendo]= 26 = 13 = 13 : 14 28 14 Correct Option: A
x = 3 ⇒ x3 = 27 y 1 y3 1 ⇒ x3 − y3 = 27 − 1 x3 − y3 27 + 1
[By componendo and dividendo]= 26 = 13 = 13 : 14 28 14
- If a : b = c : d = e : f = 1 : 2, then (pa + qc + re) : (pb + qd + rf) is equal to :
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a = c = e = 1 b d f 2 ⇒ pa = qc = re = 1 pb qd rf 2 ⇒ pa + qc + re = 1 or 1 : 2 pb + qd + rf 2 Correct Option: D
a = c = e = 1 b d f 2 ⇒ pa = qc = re = 1 pb qd rf 2 ⇒ pa + qc + re = 1 or 1 : 2 pb + qd + rf 2
- If p : q = r : s = t : u = 2 : 3, then (mp + nr + ot) : (mq + ns +ou) is equal to :
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If a = c = e , then each of b d f these ratios is equal to a + c + e b + d + f
Here,p = r = t = 2 q s u 3 ⇒ mp = nr = ot = 2 mq ns ou 3 ⇒ mp + nr + ot : 2 or 2 : 3 mq + ns + ou 3 Correct Option: C
If a = c = e , then each of b d f these ratios is equal to a + c + e b + d + f
Here,p = r = t = 2 q s u 3 ⇒ mp = nr = ot = 2 mq ns ou 3 ⇒ mp + nr + ot : 2 or 2 : 3 mq + ns + ou 3
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then x : y : z, is equal to :If x = 1 y and y = 1 z 3 2
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x = 1 y ⇒ x : y = 1 : 3 3 Again, y = 1 z ⇒ y : z 2
= 1 : 2 = 3 : 6
∴ x : y : z = 1 : 3 : 6Correct Option: C
x = 1 y ⇒ x : y = 1 : 3 3 Again, y = 1 z ⇒ y : z 2
= 1 : 2 = 3 : 6
∴ x : y : z = 1 : 3 : 6
- If a : b = 7 : 9 and b : c =15 : 7, then what is a : c?
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a : c = (a : b) × (b : c)
= 7 × 15 = 15 = 5 : 3 9 7 9
Second Method :
A : C = 7 × 15 : 9 × 7 = 5 : 3Correct Option: A
a : c = (a : b) × (b : c)
= 7 × 15 = 15 = 5 : 3 9 7 9
Second Method :
A : C = 7 × 15 : 9 × 7 = 5 : 3