Ratio and Proportions Questions and answers

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Aptitude

11). Rs 5625 is divided among A,B and C so that A may received 1 / 2 as much as B and C together receive and B received 1 / 4 of what A and C together receive. The share of A is more than that of B by

A). Rs. 750

B). Rs. 775

C). Rs. 1500

D). Rs. 1600

View Answer

12). The students of three classes are in the ratio 3 : 4 : 5. If 15 students are increased in each class, then ratio changes to 6 : 7 : 8. The total number of students before the increase was

A). 70

B). 90

C). 120

D). 60

View Answer

Correct Answer: 60

Let the number of students be 3x, 4x and 5x.
Then (3x + 15) : (4x + 15) : (5x +15) = 6 : 7 : 8

\( \Large \frac{3x + 15}{6} = \frac{4x + 15}{7} \)

= \( \Large\frac{5x + 15}{8} \)

= > 7(3x +15) = 6(4x + 15)
X = 5
Total number of students before increase = >12x = 60

13). If a cone is divided in two parts by drawing a plane through mid - point of its axis, then ratio of the volumes of the 2 parts of the cone is

A). 1 : 2

B). 1 : 4

C). 1 : 7

D). 1 : 8

View Answer

Correct Answer: 1 : 7

Let PQ be the plane which passes through middle point O of the axis AO of the cont(A,BC).

Let r be the radius of the cone (A, PQ) and h its height. Then, from geometry, radius of the cone (A,BC) is 2r and its height is 2h.

Volume of the cone (A, PQ) = \( \Large\frac{1}{3} \pi r^2 h \)

Volume of the cone (A,B,C)

= \( \Large\frac{1}{3} \pi r^2.(2r)^2(2h)\)

= \( \Large\frac{8}{3} \pi r^2 h\)

Volume of the portion (PB, OC) = Volume of the cone (A, BC) - Volume of the cone (A, PQ)

= \( \Large\frac{8}{3} \pi r^2 h\) - \( \large\frac{1}{3} \pi r^2 h\)

= \( \Large\frac{7}{3} \pi r^2 h\)

Required ratio = \( \Large\frac{ \Large\frac{1}{3} \pi r^2 h }{\large\frac{7}{3} \pi r^2 h} \)
= 1/ 7 = 1 : 7

14). A sum of money is divided among A,B, C so that to each rupee A gets , B gets 75 paise and C gets 45 paise. If C's share is Rs. 81, the sum is

A). Rs. 326

B). Rs. 639

C). Rs. 396

D). Rs. 369

View Answer

15). Rs.624 has been divided among A, B, C in such a way that if their shares be diminished by Rs. 7, Rs. 8 and Rs. 9 respectively, the remainders are in the ratio 1 : 2 : 3. Then A's share is

A). Rs. 170

B). Rs.117

C). Rs.71

D). Rs.107

View Answer

16). A and B are two alloys of gold and copper prepared by mixing metals in the proportions 7 : 2 and 7 : 11 respectively. If equal quantities of the alloys are melted to form a third alloy C, proportion of gold and copper in C will be

A). 5 : 7

B). 5 : 9

C). 9 : 5

D). 7 : 5

View Answer

Correct Answer: 7 : 5

Gold in C = \( \Large \left( \frac{7}{9} + \frac{7}{18} \right) \)

= \( \Large\frac{21}{18} = \frac{7}{6} \)

Copper in C = \( \Large \left( \frac{2}{9} + \frac{11}{18} \right) \)

= \( \Large\frac{15}{18} = \frac{5}{6} \)

Gold : Copper = \( \Large\frac{7}{6} : \frac{5}{6} \)

= 7 : 5

17). 24 litre of a mixture contains milk and water in the ration 7 : 5. How much more water is to be added to get a new mixture containing milk and water in the ratio of 5 : 7?

A). 10 litre

B). 6.9 litre

C). 9 litre

D). 9.6 litre

View Answer

Correct Answer: 9.6 litre

Milk = \( \Large \left( 24 \times \frac{7}{12} \right) \)
=l4 litres

Water = \( \Large \left( 24 \times \frac{5}{12} \right) \)
= 10 litres

\( \Large\frac{14}{10 + x} = \frac{5}{7} \)

= > 7 X 14 = 50 + 5x
= > x = 9.6 litres

18). If two spheres have their radii in the ratio 2 :3, then ratio of their volumes is

A). 8 : 27

B). 4 : 9

C). 6 : 12

D). 1 : 15

View Answer

19). The diameter of two cones are one metre each. Their curved surface are 198\(m^2 \) and 220\(m^2 \). The ratio of their slant height is

A). 7: 9

B). 8 : 9

C). 9 : 10

D). 10 : 11

View Answer

Correct Answer: 9 : 10

Diameter of each cone = 1m
Radius of each cone = 1/ 2 m

Let l1 and l2 be slant heights of the cones,
Then

\( \Large \frac{\pi \frac{1}{2}l_1}{\pi \frac{1}{2}l_2} = \frac{198}{220} \)

\( \Large \frac{l_1}{l_2} = \frac{9}{10} \)

11 : 12 = 9 :10

20). Two cylinders of equal volumes have their heights in the ratio 2 : 3. The ratio of their radii is

A). 1 : 3

B). \( \sqrt{3} : 2 \)

C). 3 : \( \sqrt{2} \)

D). \( \sqrt{3} :\sqrt{2} \)

View Answer

Correct Answer: \( \sqrt{3} :\sqrt{2} \)

Let height of first cylinder be 2h. Then the height of second cylinder is 3h. Let the radius of first and second cylinder be r1 and r2 respectively.

Volume of the first cylinder = \( \Large \pi r_1^2.(2h) \)

Volume of second cylinder = \( \Large \pi r_2^2.(3h) \)

\( \Large \pi r_1^2.(2h) \) = \( \Large \pi r_2^2.(3h) \)

\( \Large 2r_1^2 = 3r_2^2 \)

\( \Large \frac{r_1^2}{ r_2^2} = \frac{3}{2} \)

\( \Large \frac{r_1}{r_2} = \frac{\sqrt{3}}{\sqrt{2}} \)

\( r_1 : r_2 = \sqrt{3} : \sqrt{2} \)

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