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CTET Mixture & Alligation Questions with Answers & Explanations

18 Mixture & Alligation questions from the Mathematics section of CTET, each with the correct answer and a worked explanation. Try each question first, then tap Show answer to check. When you're ready, take the timed chapter-wise test to see your all-India rank.

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Question 1

In what ratio must rice at ₹15/kg be mixed with rice at ₹25/kg so that the mixture costs ₹24/kg?

  1. A1 : 9
  2. B9 : 1
  3. C3 : 5
  4. D2 : 9
Show answer
Answer: (A) 1 : 9 By alligation, ratio = (25 − 24) : (24 − 15) = 1 : 9.
Question 2

In what ratio must rice at ₹15/kg be mixed with rice at ₹25/kg so that the mixture costs ₹17/kg?

  1. A9 : 2
  2. B1 : 4
  3. C4 : 1
  4. D3 : 5
Show answer
Answer: (C) 4 : 1 By alligation, ratio = (25 − 17) : (17 − 15) = 4 : 1.
Question 3

In what ratio must rice at ₹24/kg be mixed with rice at ₹36/kg so that the mixture costs ₹29/kg?

  1. A7 : 5
  2. B8 : 5
  3. C1 : 1
  4. D5 : 7
Show answer
Answer: (A) 7 : 5 By alligation, ratio = (36 − 29) : (29 − 24) = 7 : 5.
Question 4

In what ratio must rice at ₹15/kg be mixed with rice at ₹25/kg so that the mixture costs ₹18/kg?

  1. A8 : 3
  2. B3 : 5
  3. C7 : 3
  4. D1 : 1
Show answer
Answer: (C) 7 : 3 By alligation, ratio = (25 − 18) : (18 − 15) = 7 : 3.
Question 5

In what ratio must rice at ₹15/kg be mixed with rice at ₹25/kg so that the mixture costs ₹22/kg?

  1. A4 : 7
  2. B3 : 7
  3. C1 : 1
  4. D7 : 3
Show answer
Answer: (B) 3 : 7 By alligation, ratio = (25 − 22) : (22 − 15) = 3 : 7.
Question 6

In what ratio must rice at ₹50/kg be mixed with rice at ₹80/kg so that the mixture costs ₹62/kg?

  1. A2 : 3
  2. B3 : 2
  3. C1 : 1
  4. D5 : 8
Show answer
Answer: (B) 3 : 2 By alligation, ratio = (80 − 62) : (62 − 50) = 3 : 2.
Question 7

In what ratio must rice at ₹50/kg be mixed with rice at ₹80/kg so that the mixture costs ₹67/kg?

  1. A5 : 8
  2. B1 : 1
  3. C13 : 17
  4. D17 : 13
Show answer
Answer: (C) 13 : 17 By alligation, ratio = (80 − 67) : (67 − 50) = 13 : 17.
Question 8

In what ratio must rice at ₹50/kg be mixed with rice at ₹80/kg so that the mixture costs ₹54/kg?

  1. A5 : 8
  2. B13 : 2
  3. C1 : 1
  4. D27 : 4
Show answer
Answer: (B) 13 : 2 By alligation, ratio = (80 − 54) : (54 − 50) = 13 : 2.
Question 9

In what ratio must rice at ₹30/kg be mixed with rice at ₹45/kg so that the mixture costs ₹37/kg?

  1. A8 : 7
  2. B7 : 8
  3. C9 : 7
  4. D2 : 3
Show answer
Answer: (A) 8 : 7 By alligation, ratio = (45 − 37) : (37 − 30) = 8 : 7.
Question 10

In what ratio must rice at ₹30/kg be mixed with rice at ₹45/kg so that the mixture costs ₹32/kg?

  1. A13 : 2
  2. B7 : 1
  3. C2 : 13
  4. D2 : 3
Show answer
Answer: (A) 13 : 2 By alligation, ratio = (45 − 32) : (32 − 30) = 13 : 2.

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Question 11

In what ratio must rice at ₹30/kg be mixed with rice at ₹45/kg so that the mixture costs ₹44/kg?

  1. A2 : 3
  2. B14 : 1
  3. C1 : 14
  4. D1 : 1
Show answer
Answer: (C) 1 : 14 By alligation, ratio = (45 − 44) : (44 − 30) = 1 : 14.
Question 12

In what ratio must rice at ₹24/kg be mixed with rice at ₹36/kg so that the mixture costs ₹28/kg?

  1. A9 : 4
  2. B2 : 3
  3. C1 : 1
  4. D2 : 1
Show answer
Answer: (D) 2 : 1 By alligation, ratio = (36 − 28) : (28 − 24) = 2 : 1.
Question 13

In what ratio must rice at ₹20/kg be mixed with rice at ₹30/kg so that the mixture costs ₹21/kg?

  1. A1 : 1
  2. B10 : 1
  3. C9 : 1
  4. D1 : 9
Show answer
Answer: (C) 9 : 1 By alligation, ratio = (30 − 21) : (21 − 20) = 9 : 1.
Question 14

In what ratio must rice at ₹40/kg be mixed with rice at ₹60/kg so that the mixture costs ₹48/kg?

  1. A1 : 1
  2. B3 : 2
  3. C2 : 3
  4. D13 : 8
Show answer
Answer: (B) 3 : 2 By alligation, ratio = (60 − 48) : (48 − 40) = 3 : 2.
Question 15

In what ratio must rice at ₹30/kg be mixed with rice at ₹45/kg so that the mixture costs ₹41/kg?

  1. A11 : 4
  2. B1 : 1
  3. C4 : 11
  4. D2 : 3
Show answer
Answer: (C) 4 : 11 By alligation, ratio = (45 − 41) : (41 − 30) = 4 : 11.
Question 16

In what ratio must rice at ₹30/kg be mixed with rice at ₹45/kg so that the mixture costs ₹39/kg?

  1. A3 : 2
  2. B7 : 9
  3. C1 : 1
  4. D2 : 3
Show answer
Answer: (D) 2 : 3 By alligation, ratio = (45 − 39) : (39 − 30) = 2 : 3.
Question 17

In what ratio must rice at ₹20/kg be mixed with rice at ₹30/kg so that the mixture costs ₹24/kg?

  1. A7 : 4
  2. B2 : 3
  3. C3 : 2
  4. D1 : 1
Show answer
Answer: (C) 3 : 2 By alligation, ratio = (30 − 24) : (24 − 20) = 3 : 2.
Question 18

In what ratio must rice at ₹40/kg be mixed with rice at ₹60/kg so that the mixture costs ₹56/kg?

  1. A1 : 1
  2. B2 : 3
  3. C1 : 4
  4. D4 : 1
Show answer
Answer: (C) 1 : 4 By alligation, ratio = (60 − 56) : (56 − 40) = 1 : 4.

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