LTI Ratio and Proportion Quiz 1

Let Water bill = 5x , Grocery = 2x and salon=3x
New Water bill expenditure= \frac{104}{100} \times 5x = \frac{52x}{10}
New grocery expenditure = \frac{107}{100} \times 2x = \frac{214x}{100}
New salon expenditure = \frac{108}{100} \times 3x = \frac{324x}{100}
New ratio = \frac{52x}{10} : \frac{214x}{100} : \frac{324x}{100} = 260 : 107: 162

Let the number of 25p coins = x
Number of 50p coins = 500 - x
x \times \frac{25}{100} + (500-x)\times \frac{50}{100} = Rs.\ 150

Solving this, we get x = 200
50p coins are = 500 - 200 = 300

Let Jack and Jill’s present ages be x and y respectively

According to the question,
2 years ago, their ages were (x-2) and (y-2) respectively.
2 years hence, their ages will be (x+2) and (y+2) respectively.

The two equations produced are:

\frac{x-2}{y-2}=\frac{1}{2}
\frac{x+2}{y+2}=\frac{2}{3}

Solving these equations,we get
x=6 years
y=10 years

Circumference of square = 4 x side of square =76m
Side of square = 19m
Circumference of circle = 2\prod x radius of circle = 76m
Radius of circle = \frac{38}{\prod}
Area of square = 19 x 19 = 369
Then, Area of square : Radius of circle = 369 : \frac{38}{\prod} = \frac{19\prod}{2}

Let the numbers be x, 2x and 3x respectively.

According to the question,
x^{2}+(2x)^{2}+(3x)^{2} = 50,176
x^{2}+4x^{2}+9x^{2} = 50,176

14x = 50,176
x=3,584
The smallest number is x = 3,584

If 48 men can build a tower in 9 days
1 man can build the tower in = 48 x 9 days
24 men can build the tower in = (48 x 9) / 24 days = 18 days

5% of n1 + 6% of n2 = \frac{2}{3} (9% of n1 + 8% of n2)
[18-16] % of n2 = [18-15] % of n1
2 % of n2 = 3% of n1
n1 : n2 = 2:3

Graduates = 7x
Postgraduates = 3x
Total = 7x + 3x = 10x

Graduates who have scholarship = 20% of 7x = \frac{14}{10}x

Postgraduates who have scholarship = 30% of 3x = \frac{9}{10}x

Total scholarship holders = \frac{14}{10}x + \frac{9}{10}x = \frac{23}{10}x

Non- scholarship holders = Total students - Scholarship holders =

10x - \frac{23}{10}x=\frac{77}{10}x

% of Non-scholarship holders =

\frac{Non-Scholarship\ students}{Total\ students}\times 100
\frac{\frac{77}{10}x}{10x}\times 100 = \frac{77}{100} = 77%

Assume that the daily wages of man, women and daughter are Rs 5x, Rs. 4x, Rs 3x respectively.
Multiply (no. of days) with (assumed daily wage) of each person to calculate the value of x.
[3 x (5x)] + [2 x (4x)] + [4 x (3x)] = 105
[15x + 8x + 12x] = 105
35x = 105
x = 3
Hence, man's daily wage = 5x = 5 x 3 = Rs. 15
Wife's daily wage = 4x = 4 x 3 = Rs. 12
Daughter's daily wage = 3x = 3 x 3 = Rs. 9

\frac{Rajat's age}{Rohan 's age}= \frac{Present age of Rajat +x}{Present age of Rohan +x} = \frac{24+x}{30+x}=\frac{5}{6}

Solving the equation, we get x=6.

Therefore, their ages will be in the ratio 2:3 after 6 years.