Robert Bosch Ratio & Proportion Quiz 3

Answer: c.
Explanation:
Let the number of boys and girls are 7x and 5x, respectively.
Given, total number of students = 2400
7x + 5x = 2400 ⇒ 12x = 2400
∴ x = 200
∴ Required number of girls = 5x = 5 × 200 = 1000

Answer: b.
Explanation:
In 400 gm alloy,
Zinc = (⅝) x 400 = 250 gm, Copper = 400 – Zinc = 150 gm
If x gm of copper be mixed, then
=(\frac{250}{150+x}) = \frac{5}{4}
750 + 5x = 1000
⇒ 5x = 1000 – 750 = 250
⇒ x = 50 gm.

Answer: b.
Explanation:
Let the total wealth be Rs. 100. Amount to be given to the son-in-law and the daughter = (3 / 5) x 100 = 60
The given ratio of amount of the son-in-law and the daughter = 1 : 4
∴ Amt. to be given to the daughter = (4 / 5) x 60 = 48
∴ Amt. to be donated to the NGO = (1 / 2 ) x 48 = 24
Now, remaining amount = 100 – 60 – 24 = 16 Amt. to be given to wife = (1 / 4) x 16 = 4
The final remaining amount = 16 – 4 = 12
Applying the rule of proportion here, we get Since, 12 ≡ 16800
∴ 24 (the amount donated to the NGO) ≡ X
∴ X = \frac{16800}{12}\times24 = 33600

Answer: c.
Explanation:Ratio of each piece of diamond = 2x : 3x : 4x
∴ Solid crystal diamond = 2x + 3x + 4x = 9x
∴ Cost of solid crystal diamond = (9x)2 = 81x2
Cost of broken pieces of diamond = (2x)2 + (3x)2 + (4x)2 = 29x2
∴ Loss = 81x2 – 29x2 = 52x2
Given, 81x2 = 24300
x^{2}=\frac{24300}{81}=300
∴ Loss = 52 × 300 = Rs. 15600

Answer: b.
Let a year ago i.e. in 2016 Madlyn and Lawrence’s salaries were x and y and now it is m and n respectively.
Given that,
\frac{x}{y}=\frac{2}{3}.......(1)
\frac{x}{m}=\frac{3}{4}.......(2)
\frac{y}{n}=\frac{5}{7}.......(3)
From (i) and (ii),
\frac{m}{y}=\frac{2\times4}{3\times3}=\frac{8}{9}...........(4)
From (iii) and (iv)
\frac{m}{y}=\frac{8\times5}{9\times7}=\frac{40}{63}
\frac{n}{m}=\frac{63}{40}
\frac{n}{m}-1=\frac{63}{40}-1
\frac{n-m}{m}=\frac{63-40}{40}
\frac{n-m}{m}=\frac{23}{40}...........(5)
Also, given that (n – m) = 2300
Putting the value In equation (5)
\frac{2300}{m}=\frac{23}{40}
m=\frac{40\times 2300}{23}=4000
So, n = 4000 + 2300 = 6300

Answer:
Explanation:
Let the First-year income of Alexandra= 2x
And, Second-year income of Alexandra = 3x
Now, Acc. To Question: The 2nd year income = 45000
So, x = 45000 / 3 = 15000
Therefore, 1st year income = 2 x 15000 = 30000
Similarly, Let the 1st Year expenditure = 5y
And Acc. to Question : 1st Year expenditure =25000
So, y = 25000/5 = 5000
Second-year expenditure = 9y= 9* 5000 = 45000
Using Formula:
Income = expenditure + savings, savings = income - expenditure
Therefore, 1st year savings = 30000- 25000 = 5000
Similarly, 2nd year savings = 45000- 45000 = 0
Now, total saving in two years = first-year savings + second-year savings,
Total saving = 5000+0 = 5000 Rs

Answer: a.
Explanation:
Let the investment of Leonard be ₹ X, that of Sheldon be ₹ Y and that of Howard be ₹ Z respectively.
Then, 12X : 9Y : 6Z = 7 : 8 : 9 or or,\frac{12X}{9Y}=\frac{7}{8}
∴ 32X = 21Y , \frac{21}{32}Y
And,\frac{9Y}{6Z}=\frac{8}{9}
∴ 27Y = 16Z , \frac{27}{16}Y
So, X:Y:Z=\frac{21}{32}Y:Y:\frac{27}{16}Y=21:32:54

Answer: d.
Explanation:
Let,
Marks obtained by Jane Foster theory and total marks of theory be ‘7X’ and ‘10X’ respectively

So, total marks (theory + practical) = 10X + 2X = 12X
Marks obtained by Jane (theory + practical) = 7X + 2X = 9X
Required Ratio = \frac{9X}{12X}=\frac{3}{4}

Answer: b.
Explanation: The number of employees = 3 : 2 The salary of each employee: 4 : 5 Then the expenditure will be: 4*3 = 12 : 2*5 = 10
12 (initial expenditure): 10 (final expenditure) Or, if the final expenditure = 10, that means the initial expenditure was 12.
Therefore total expenditure reduced by = 12 - 10 = 2 Units
Or, 2 units = 12000 (According to the question, Rs 12000 is saved by the company) So, 1 unit = 6000
Now, the initial expenditure on salary = 12 units * 6000 = Rs.72000

Answer: d.
Explanation:
Let the Hunter Bike is rented for 8 hours or less
Then the number of hours it is rented for,
= 800 / 100 = 8 Hrs

But if he got charged Rs. 8 per km, the amount that he should paid be 120 x 8 = 960
But he paid only Rs. 800
The bike is rented for more than 8 hours,
Number of Hours = \frac{800}{80}=10 Hrs

If he is charged at Rs. 6 per km.
The amount that he should pay is 120(6) = Rs. 720 which is less than Rs 800

Therefore, Clark rented the bike for 10 hours.