Ratio, Proportion
- If A : B = 3 : 5 and B : C = 4 : 7, then A :B : C is
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A : B = 3 : 5 = 12 : 20
B : C = 4 : 7 = 20 : 35
∴ A : B : C = 12 : 20 : 35
Second Method :
A : B : C = xp : yp : qy
= 3 × 4 : 5 × 4 : 5 × 7
= 12 : 20 : 35Correct Option: D
A : B = 3 : 5 = 12 : 20
B : C = 4 : 7 = 20 : 35
∴ A : B : C = 12 : 20 : 35
Second Method :
A : B : C = xp : yp : qy
= 3 × 4 : 5 × 4 : 5 × 7
= 12 : 20 : 35
- If A and B are in the ratio 3 : 4, and B and C in the ratio 12 : 13, then A and C will be in the ratio
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A : B = 3 : 4 = 9 : 12
B : C = 12 : 13
∴ A : B : C = 9 : 12 : 13
⇒; A : C = 9 : 13
Second Method :
A : C = xp : yq
= 3 × 12 : 4 × 13
= 9 : 13Correct Option: B
A : B = 3 : 4 = 9 : 12
B : C = 12 : 13
∴ A : B : C = 9 : 12 : 13
⇒; A : C = 9 : 13
Second Method :
A : C = xp : yq
= 3 × 12 : 4 × 13
= 9 : 13
- If x : y = 4 : 5, then (3x + y) : (5x + 3y) =
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x = 4 y 5 ∴ 3x + y 5x + y = 3 
x 
+ 1 y 5 x + 3 y = 3 × 4 + 1 5 5 × 4 + 3 5 = 12 + 5 5 7 = 17 = 17 : 35 35 Correct Option: C
x = 4 y 5 ∴ 3x + y 5x + y = 3 x + 1 y 5 x + 3 y = 3 × 4 + 1 5 5 × 4 + 3 5 = 12 + 5 5 7 = 17 = 17 : 35 35
- If A : B is 2 : 3, B : C is 6 : 11, then A : B : C is :
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A : B = 2 : 3 = 4 : 6
B : C = 6 : 11
∴ A : B : C = 4 : 6 : 11
Second Method :
A : B : C = xp : yp : qy
= 2 × 6 : 3 × 6 : 3 × 11
= 12 : 18 : 33
= 4 : 6 : 11Correct Option: C
A : B = 2 : 3 = 4 : 6
B : C = 6 : 11
∴ A : B : C = 4 : 6 : 11
Second Method :
A : B : C = xp : yp : qy
= 2 × 6 : 3 × 6 : 3 × 11
= 12 : 18 : 33
= 4 : 6 : 11
- The ratio of weekly income of A and B is 9 : 7 and the ratio of their expenditures is 4 : 3. If each saves ₹ 200 per week, then the sum of their weekly income is
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Let A’s and B’s weekly income be ₹ 9x and ₹ 7x and their expenditures be ₹ 4y and 3y respectively.
Then, 9x – 4y = 200 ...(i)
and 7x – 3y = 200 ...(ii)
⇒ 9x – 4y = 7x – 3y
⇒ 9x – 7x = 4y – 3y
⇒ 2x = y ...(iii)
From equation (i),
9x – 4y = 200
⇒ 9x – 8x = 200
⇒ x = 200
∴ Sum of their weekly income
= 16x = 16 × 200 = ₹ 3200Correct Option: B
Let A’s and B’s weekly income be ₹ 9x and ₹ 7x and their expenditures be ₹ 4y and 3y respectively.
Then, 9x – 4y = 200 ...(i)
and 7x – 3y = 200 ...(ii)
⇒ 9x – 4y = 7x – 3y
⇒ 9x – 7x = 4y – 3y
⇒ 2x = y ...(iii)
From equation (i),
9x – 4y = 200
⇒ 9x – 8x = 200
⇒ x = 200
∴ Sum of their weekly income
= 16x = 16 × 200 = ₹ 3200
