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The income of A, B and C are in the ratio 7 : 9 : 12 and their spending are in the ratio 8 : 9 : 15. If A saves $$\frac{1}{4}$$ th of his income then the savings of A, B and C are in the ratio of = ?
Answer & Solution
Correct Answer:
Option
A
Let income of A, B and C are 7x, 9x and 12x respectively
and expenditure of A, B and C are 8y, 9y and 15y respectively
$$\eqalign{ & \Rightarrow {\text{Income}}\,{\text{of,}} \cr & A \times \frac{1}{4} = {\text{Saving}}\,{\text{of}}\,{\text{A}}\,\left( {{\text{given}}} \right) \cr & \Rightarrow 7x - 8y = 7x \times \frac{1}{4} \cr & \Rightarrow 28x - 32y = 7x \cr & \Rightarrow 21x = 32y \cr & \Rightarrow x:y = 32:21 \cr} $$
∴ The ratio of savings of A, B and C
⇒ (7x - 8y) : (9x - 9y) : (12x - 15y)
⇒ (7 × 32 - 8 × 21) : (9 × 32 - 9 × 21) : (12 × 32 - 15 × 21)
⇒ (224 - 168) : (288 - 189) : (384 - 315)
⇒ 56 : 99 : 69
and expenditure of A, B and C are 8y, 9y and 15y respectively
$$\eqalign{ & \Rightarrow {\text{Income}}\,{\text{of,}} \cr & A \times \frac{1}{4} = {\text{Saving}}\,{\text{of}}\,{\text{A}}\,\left( {{\text{given}}} \right) \cr & \Rightarrow 7x - 8y = 7x \times \frac{1}{4} \cr & \Rightarrow 28x - 32y = 7x \cr & \Rightarrow 21x = 32y \cr & \Rightarrow x:y = 32:21 \cr} $$
∴ The ratio of savings of A, B and C
⇒ (7x - 8y) : (9x - 9y) : (12x - 15y)
⇒ (7 × 32 - 8 × 21) : (9 × 32 - 9 × 21) : (12 × 32 - 15 × 21)
⇒ (224 - 168) : (288 - 189) : (384 - 315)
⇒ 56 : 99 : 69
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LoginIncome = 7x:9x:12x
Spending = 8y:9y:15y
Saved: 7x-8y: 9x-9y: 12x-15y
7x-8y = 7x / 4
y = 21x/32
9x - 9y = 99x/32
12x-15y = 69x/32
Saved: 7x/4:99x/32:69x/32 = 56:99:69
if u assume x and y and solving u will be annoyed.
Provided 1/4 is the saving, 3/4 is the expenditure
so Expenditure=3, Income = 4
first make A’s Income and Expenditure ratio parts as below
A
7*8 9*7 12*7
8*7 9*7 15*7
Now make first one as 4 parts by multiplying 4 and second make 3 parts by multiplying 3
A’s Income = 7*8*4 = 224
A’s Expenditure = 8*7*3=168 Saving = 56
Now
B’s Income = 9*8*4 = 288
B’s Expenditure = 9*7*3=189 Saving = 99
A’s Income = 12*8*4 = 384
B’s Expenditure = 15*7*3=315 so Saving = 69
Ratio 56:99:69.
In hurry i haven’t written in detail. solve this way it will save lot of time