Ratio, Proportion & Variation - SSC

Person A started a business by investing ₹65,000. After a few months. B joined him by investing ₹50.000. Three months after the joining of B, C joined the two with an investment of ₹55.000. At the end of the year. A got 50% of profit as his share. For how many months did A alone finance the business?

• A.

  2

• B.

  3

• C.

  5

• D.

  4

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The ratio of the sum of and the difference between two numbers is 6 : 5. Find the ratio of these two numbers.

• A.

  3 : 2

• B.

  7 : 5

• C.

  2 : 3

• D.

  11 : 1

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Calculate the third proportional to 4, 15 and 24.

• A.

  $\frac{32}{5}$

• B.

  $\frac{29}{5}$

• C.

  $\frac{21}{5}$

• D.

  $\frac{26}{5}$

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In a 1200 m race, the ratio of the speeds of two contestants Meenal and Nitu is 5:7. If Meenal has a start of 500 m,then Meenal wins by:

• A.

  220 m

• B.

  240 m

• C.

  250 m

• D.

  225 m

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Find the ratio in which pulses at ₹80 per kg can be mixed with pulses at ₹95 per kg to get a mixture worth ₹85 per kg.

• A.

  2 : 5

• B.

  1 : 2

• C.

  2 : 1

• D.

  3 : 2

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Find the 3rd proportional to 9 and 21.

• A.

  49

• B.

  12

• C.

  30

• D.

  81

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Champa buys type 1 sugar at ₹45 per kg. He mixes it with type 2 sugar having a price of ₹48 per kg. The final mixture becomes worth ₹46 per kg. What is the ratio of the quantities of type 1 sugar to type 2 sugar in the final mixture?

• A.

  1 : 2

• B.

  2 : 3

• C.

  3 : 2

• D.

  2 : 1

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If ABC is a triangle in which DE ‖ BC and AD ∶ DB = 9 ∶ 8, then DE : BC is _________.

• A.

  9 : 17

• B.

  9 : 15

• C.

  8 : 17

• D.

  9 : 13

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A beaker is filled with a liquid, 3 parts of which are water and 7 parts some medicine. What part of the mixture should be replaced with water so that that the resultant mixture has water and medicine in a ratio 1:1?

• A.

  $\frac{1}{7}$

• B.

  $\frac{2}{7}$

• C.

  $\frac{2}{5}$

• D.

  $\frac{1}{5}$

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Find the fourth proportional to 7, 13 and 21.

• A.

  26

• B.

  39

• C.

  14

• D.

  21

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If the radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 3, then the ratio of their volumes is:

• A.

  22 : 15

• B.

  20 : 27

• C.

  3 : 4

• D.

  16 : 23

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A and B share a few marbles in the ratio 4 : 5. If B gets 10 marbles more than A, then what is A’s share?

• A.

  8 marbles

• B.

  42 marbles

• C.

  12 marbles

• D.

  40 marbles

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What is the third proportion to 15 and 24?

• A.

  38$\frac{4}{5}$

• B.

  37$\frac{2}{5}$

• C.

  38$\frac{2}{5}$

• D.

  37$\frac{4}{5}$

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Soham’s initial expenditure and savings were in the ratio 5: 1. His income increases by 25%, while his savings increase by 20%. If Soham’s current expenditure is ₹4,347, what was his initial income?

• A.

  ₹4,130

• B.

  ₹4,140

• C.

  ₹4,150

• D.

  ₹4,160

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If a ∶ b = 2 ∶ 3 and b ∶ c = 6 ∶ 8, then find a ∶ b ∶ c.

• A.

  2 ∶ 3 ∶ 5

• B.

  2 ∶ 3 ∶ 4

• C.

  1 ∶ 2 ∶ 3

• D.

  2 ∶ 3 ∶ 6

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In what ratio must a grocer mix two varieties of pulses costing ₹15 and ₹20 per kg, respectively, so as to get a mixture worth ₹18 per kg?

• A.

  3 : 2

• B.

  3 : 4

• C.

  2 : 3

• D.

  2 : 5

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In a bag, black tablet covers and white tablet covers are in the ratio 5:9. If there are 450 white tablet covers, how many black tablet covers are there in the bag?

• A.

  200

• B.

  275

• C.

  225

• D.

  250

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A beaker contains a mixture of two liquids X and Y in the ratio 5 : 3. When 6 litres of the mixture is drawn off and then replaced with Y, the ratio of X and Y becomes 5 : 7.
How many litres of liquid X was contained in the beaker initially?

• A.

  18.25

• B.

  22.5

• C.

  11.25

• D.

  15.5

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The fourth proportional to 5, 8 and 30 is:

• A.

  50

• B.

  60

• C.

  48

• D.

  90

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If P : Q = 10 ∶11 and Q ∶ R = 11 ∶ 12, then P + Q ∶ Q + R ∶ R + P is:

• A.

  21 ∶ 23 ∶ 22

• B.

  22 ∶ 21 ∶ 23

• C.

  11 ∶ 12 ∶ 10

• D.

  23 ∶ 22 ∶ 21

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A triangle with the lengths of its sides proportional to the numbers 7, 24 and 30 is:

• A.

  acute angled

• B.

  not possible

• C.

  obtuse angled

• D.

  right angled

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Numbers A and B are 0% and 50%, respectively, more than the number C. The ratio of A to that of B is:

• A.

  13 : 15

• B.

  4 : 5

• C.

  15 : 13

• D.

  5 : 4

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An amount of ₹1,003 is to be distributed among A, B and C in the ratio of 11 : 23 : 25. How many rupees would B get more than A?

• A.

  ₹238

• B.

  ₹29

• C.

  ₹187

• D.

  ₹204

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Three numbers are in the proportion of 3 : 8 : 15 and their LCM is 8280. What is their HCF?

• A.

  60

• B.

  57

• C.

  69

• D.

  75

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The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8. then the third number is:

• A.

  30

• B.

  20

• C.

  49

• D.

  48

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