SSC CGL 20201)If 3A = 4B = 5C, then A : B : C is equal to :

Correct Option: C

20 : 15 : 12

let 3A = 4B = 5C = K

\(A= {K \over 3}, B= {K \over 4}, C= {K \over 5}\)

\(A:B:C = {K \over 3} : {K \over 4}: {K \over 5}\)

\(= {1 \over 3} : {1 \over 4}: {1 \over 5}\)

=20:15:12

SSC CGL 20192)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?

Correct Option: C

\(xb^2 : ya^2\)

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 20193)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 :

Correct Option: B

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 20194)If (a +b) : (b + c) : (c + a) = 7 : 6 : 5 and a + b + c = 27, then what will be the value of \(1\over a \) : \(1\over b \) : \(1\over c\) ?

Correct Option: 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 20195)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)?

Correct Option: C

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 20196)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?

Correct Option: C

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 20197)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 :

Correct Option: D

24 : 35

SSC CGL 20198)A, B and C spend 80%, 85% and 75% of their incomes, respectively. If their savings are in the ratio 8 : 9 : 20 and the difference between the incomes of A and C is ₹18,000, then the income of B is:

Correct Option: B

Let the income of A, B and C be Rs.A, Rs.B and Rs.C; since A, B, and C spend 80%, 85%, and 75% of their incomes respectively there saveing will be 20% of A, 15% of B and 25% of C respectively.

₹ 27,000

, thud there saving will 20%, 15%

Let the income of A, B and C be Rs.A, Rs.B and Rs.C; since A, B, and C spend 80%, 85%, and 75% of their incomes respectively there saveing will be 20% of A, 15% of B and 25% of C respectively.

Also, Savings are in the ratio 8 : 9 : 20 respectively.

Thus, 20% of A : 15% of B : 25% of C :: 8 : 9 : 20

From above, 20A / 25C = 8 / 20 ---(i)

It is also given, C – A = 18000 ---(ii)

Solving (i) and (ii), we get A = Rs.18000 and C = Rs.36000

Also, from 20A / 15B = 8 / 9 , we get B = Rs.27000

SSC CGL 20199)What is the ratio of the third proportional to 0.4 and 0.8, to the mean proportional between 13.5 and 0.24?

Correct Option: C

8 : 9

SSC CGL 201910)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?

Correct Option: B

5 : 4

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