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Quiz: Ratio and Proportion

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Number of Questions: 25

Question: 1 -

A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?

Options:

  1. Rs. 664

  2. Rs. 550

  3. Rs. 484

  4. Rs. 460

    5. Answer:

    Rs. 484
    Solution:

    4 A = 2 B
    15 5
     A = 2 x 15 B
    5 4
     A = 3 B
    2
    A = 3
    B 2

     A : B = 3 : 2.

     B's share = Rs. 1210 x 2 = Rs. 484.
    5

Question: 2 -

A: B: C is in the ratio of 3: 2: 5. How much money will C get out of Rs 1260?

Options:

  1. 503

  2. 125

  3. None of these

  4. 252

    5. Answer:

    None of these
    Solution:

    C's share = [C's ratio/ sum of ratios] * total amount
    C's share = (5/10) * 1260
    C's share = 630

Question: 3 -

If a: b is 3: 4 and b: c is 2: 5. Find a: b: c.

Options:

  1. 3: 6: 5

  2. 2: 3: 4

  3. 3: 2: 5

  4. 3: 4:10

    5. Answer:

    3: 4:10
    Solution:

    The ratio of a: b is 3: 4
    The ratio of b: c is 2: 5

    Note: To find the ratio in such questions, multiply a to b, then b to b, and then b to c.

    a: b: c = 3*2: 4*2: 4*5
    a: b: c = 6: 8: 20
    So, a: b: c = 3: 4: 10

Question: 4 -

A: B is 1: 2; B: C is 3: 2 and C: D is 1:3. Find A: B: C: D.

Options:

  1. 2: 1: 6: 13

  2. 3: 5: 7: 6

  3. 2: 3: 5: 7

  4. 3: 6: 4: 12

    5. Answer:

    3: 6: 4: 12
    Solution:

    ATQ,
    A: B = 1: 2........... (i)
    B: C = 3: 2...........(ii)
    C: D = 1: 3.......... (iii)
    Now,
    Find A: B: C: D
    Step 1, A: B: C: D
    1: 2 (A: B value by equation i)

    Note: To understand the shortcut, remember you need to make the right-hand side missing numbers the same as that of last given number, and for the left-hand side the same is done.

    i.e., C: D will contain 2: 2 because 2 is the last number on the right side.

    Or, A: B: C: D
    1: 2: 2: 2
    3: 3: 2: 2 (B: C value by equation ii)
    1: 1: 1: 3 (C: D value by equation iii)

    Now, multiply vertically and get A: B: C: D.

    So, A: B: C: D = (1*3*1): (2*3*1): (2*2*1): (2*2*3)
    Or, A: B: C: D = 3: 6: 4: 12

Question: 5 -

5600 is to be divided into A, B, C, and D in such a way that the ratio of share of A: B is 1: 2, B: C is 3: 1, and C: D is 2: 3. Find the sum of (A and C) and (B and C).

Options:

  1. Rs 2400, Rs 3000

  2. Rs 2000, Rs 3200

  3. Rs 2400, Rs 3200

  4. Rs 2000, Rs 3000

    5. Answer:

    Rs 2000, Rs 3200
    Solution:

    Find A: B: C: D
             1: 2: 2: 2
             3: 3: 1: 1
             2: 2: 2: 3

    Now, multiply vertically and get A: B: C: D.

    So, A: B: C: D = (1*3*2): (2*3*2): (2*1*2): (2*1*3)
    Or, A: B: C: D = 6: 12: 4: 6
    Or, A: B: C: D = 3: 6: 2: 3

    Sum of the ratios = 3+6+2+3 = 14, but ATQ, it is 5600 Rs.
    i.e., 14 * 400 = 5600
    So, multiply each and every ratio by 400 and get the share of each:
    3*400: 6*400: 2*400: 3*400
    So, the share of A = 1200
    The share of B = 2400
    The share of C = 800
    The share of D = 1200

    Now, the share of (A+C) = 1200+800 = 2000
    The share of (B+C) = 2400+ 800 = 3200