SSC CGL 20191)The ratio of the volumes of two cylinders is x : y and the ratio of their diameters is a : b. What is the ratio of their heights?
\(xb^2 : ya^2\)
The ratio of their diameters = a : b;
The ratio of their radius = a : b;
The ratio of the volumes of two cylinders = x : y;
\(\pi \times r^2h_1 : \pi \times r^2h_2 = x : y\);
\(a^2h_1 : b^2h_2 = x : y;\)
\(h_1 : h_2 = xb^2 : ya^2\)
SSC CGL 20192)The ratio of the income of A to that of B is 5 : 7. A and B save Rs.4000 and Rs.5000 respectively. If the expenditure of A is equal to 66\(2\over 3\)% of the expenditure of B, then the total income of A and B is :
Rs. 24,000
The ratio of the income of A to that of B = 5 : 7;
Let the income of A and B be 5x and 7x.
Expenditure of A = 5x - 4000;
Expenditure of B = 7x - 5000;
The expenditure of A =\( 66\frac{2}{3}\%\) of the expenditure of B,
5x - 4000 = \((7x - 5000)\times \frac{2}{3};\)
15x - 12000 = 14x - 10000;
x = 2000;
Total income of A and B = 5x + 7x = 12x = 12 \times 2000 = 24000
SSC CGL 20193)If (a +b) : (b + c) : (c + a) = 7 : 6 : 5 and a + b + c = 27, then what will be the value of \(1\over a \) : \(1\over b \) : \(1\over c\) ?
4 : 3 : 6
Let the (a + b), (b + c) and (c + a) be 7x, 6x and 5x respectively.
Now,
(a + b) + (b + c) + (c + a) = 7x + 6x + 5x;
2(a + b + c) = 18x;
Put the value of (a + b + c),
\(2 \times 27\) = 18x;
x = 3;
a + b = 7x =\( 3 \times 7\) = 21;
c = (a + b + c) - a + b = 27 - 21 = 6;
b + c = 6x = \(3 \times 6\) = 18;
b = 18 - 6 = 12;
a + b + c = 27;
a = 27 - 18 = 9;
Now,
\(\frac{1}{a} : \frac{1}{b} : \frac{1}{c} = \frac{1}{9} : \frac{1}{12} : \frac{1}{6}\)
= 4 : 3 : 6
SSC CGL 20194)When x is added to each of 2, 3, 30 and 35, then the numbers obtained in this order, are in proportion. What is the mean proportional between (x + 7) and (x - 2)?
6
Order after adding x, 2 + x, 3 + x, 30 + x, 35 + x Condition of proportion,\(\frac{2 + x}{3 + x} = \frac{30 + x}{35 + x}\) =>\((2 + x)(35 + x) = (3 + x)(30 + x) \)=>\(70 + 2x + 35x + x^2 = 90 + 3x + 30x + x^2\)=>x = 5=>Mean proportional between (x + 7) and (x - 2) = \(\sqrt{(x + 7)(x - 2)} \)=6
SSC CGL 20195)One year ago, the ratio of the age (in years) ofA to that of B was 4 : 3. The ratio of their respective ages, 3 years from now,will be 6 : 5. What will be the ratio of respective ages of A and B, 9 years from now?
9 : 8
One year ago, the ratio of the age (in years) of A to that of B = 4 : 3
After 3 year, the ratio of the age (in years) of A to that of B = 6 : 5
After 3 year, let the age of A and B are 6x and 5x.
ATQ,
\(\frac{4x + 4}{3x + 4} = \frac{6}{5}\)
20x + 20 = 18x + 24
2x = 4
x = 2
After 9 year, the ratio of the age (in years) of A to that of B = 6x + 6 : 5x + 6
\(6 \times 2 + 6 : 5 \times 2 + 6\) = 18 : 16 = 9 : 8
SSC CGL 20196)Two numbers are in the ratio 3 : 5. If 13 is subtracted from each, the new numbers are in the ratio 10 : 21, If 15 is added to each of the original numbers, then the ratio becomes :
24 : 35
SSC CGL 20197)What is the ratio of the third proportional to 0.4 and 0.8, to the mean proportional between 13.5 and 0.24?
8 : 9
SSC CGL 20198)5 years ago, the ratio of the age of A to that of B was 4 : 5. Five years hence, the ratio of the age of A to that of B will be 6 : 7. If, at present, C is 10 years younger than B, then what will be the ratio of the present age of A to that of C?
5 : 4