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15. The cost of four apples, six bananas and eight oranges is p. The cost of five apples, eight bananas and eleven oranges is q. The cost of eight apples, fourteen bananas and twenty oranges is r. Which of the following is always true? (A) (C) 3p 4q = (3r)/4; - 4q 3p = r/2 (B) - 3p 4q = 1/2 (D) - 3p 4q = r?
Most Upvoted Answer
15. The cost of four apples, six bananas and eight oranges is p. The c...
Take it into linear equations
4a+6b+7o=p   eqn1
5a+7b+9o=q     eqn2
2a+4b+3o=r     eqn3

Solve 1 and 2 to by �plying it by 2 and 5 respectively
6b-3c=5r-2q
3(2b-c) =5r-2q   

Solve 1 and 3  you get
2b-c = 2r-p

Solve above two u get 3p-2q =r
Community Answer
15. The cost of four apples, six bananas and eight oranges is p. The c...
Solution:

Given:

Cost of 4 apples + 6 bananas + 8 oranges = p ...(1)

Cost of 5 apples + 8 bananas + 11 oranges = q ...(2)

Cost of 8 apples + 14 bananas + 20 oranges = r ...(3)

To find: An equation that is always true.

Solution:

We can use the given equations to find an equation that is always true. Let's try to eliminate the variables one by one.

Eliminating oranges:

Multiplying equation (1) by 11, equation (2) by 8 and equation (3) by 5, we get:

44 apples + 66 bananas + 88 oranges = 11p ...(4)

40 apples + 64 bananas + 88 oranges = 8q ...(5)

40 apples + 70 bananas + 100 oranges = 5r ...(6)

Subtracting equation (5) from equation (4), we get:

4 apples + 2 bananas = 3p - 2q ...(7)

Subtracting equation (6) from equation (5), we get:

- 6 bananas - 12 oranges = 8q - 5r ...(8)

Eliminating bananas:

Multiplying equation (7) by 14 and adding it to equation (8) multiplied by 1, we get:

56 apples - 8 oranges = 42p - 29q + 5r ...(9)

Eliminating oranges:

Multiplying equation (1) by 20, equation (2) by 11 and equation (3) by 8, we get:

80 apples + 120 bananas + 160 oranges = 20p ...(10)

55 apples + 88 bananas + 121 oranges = 11q ...(11)

64 apples + 112 bananas + 160 oranges = 8r ...(12)

Subtracting equation (11) from equation (10), we get:

25 apples + 32 bananas + 39 oranges = 9p - 2q ...(13)

Subtracting equation (12) from equation (11), we get:

- 9 apples - 24 bananas - 39 oranges = 3q - r ...(14)

Eliminating bananas:

Multiplying equation (13) by 14 and adding it to equation (14) multiplied by 3, we get:

- 51 apples - 156 oranges = - 4p + 35q + 9r ...(15)

Multiplying equation (9) by 3, we get:

168 apples - 24 oranges = 126p - 87q + 15r ...(16)

Now, we can eliminate oranges from equations (15) and (16).

Multiplying equation (15) by 24 and adding it to equation (16) multiplied by 39, we get:

- 1236 apples = - 63p + 196q + 135r

Simplifying, we get:

3p - 4q = (3r)/4

Hence, the equation 3p - 4q = (3r)/4 is always true.

Therefore, the option (A) 3p - 4q = (3r)/4; - 4q + 3p = r/2 is correct.

Note: The other options are not true
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15. The cost of four apples, six bananas and eight oranges is p. The cost of five apples, eight bananas and eleven oranges is q. The cost of eight apples, fourteen bananas and twenty oranges is r. Which of the following is always true? (A) (C) 3p 4q = (3r)/4; - 4q 3p = r/2 (B) - 3p 4q = 1/2 (D) - 3p 4q = r?
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15. The cost of four apples, six bananas and eight oranges is p. The cost of five apples, eight bananas and eleven oranges is q. The cost of eight apples, fourteen bananas and twenty oranges is r. Which of the following is always true? (A) (C) 3p 4q = (3r)/4; - 4q 3p = r/2 (B) - 3p 4q = 1/2 (D) - 3p 4q = r? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about 15. The cost of four apples, six bananas and eight oranges is p. The cost of five apples, eight bananas and eleven oranges is q. The cost of eight apples, fourteen bananas and twenty oranges is r. Which of the following is always true? (A) (C) 3p 4q = (3r)/4; - 4q 3p = r/2 (B) - 3p 4q = 1/2 (D) - 3p 4q = r? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 15. The cost of four apples, six bananas and eight oranges is p. The cost of five apples, eight bananas and eleven oranges is q. The cost of eight apples, fourteen bananas and twenty oranges is r. Which of the following is always true? (A) (C) 3p 4q = (3r)/4; - 4q 3p = r/2 (B) - 3p 4q = 1/2 (D) - 3p 4q = r?.
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