Ratio and Proportion

Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:

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Question:
Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:

[A].

27

[B].

33

[C].

49

[D].

55

Answer: Option B

Explanation:

Let the numbers be 3x and 5x.

Then, 3x – 9 = 12
5x – 9 23

23(3x – 9) = 12(5x – 9)

9x = 99

x = 11.

The smaller number = (3 x 11) = 33.

The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?

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Question: The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?

[A].

3 : 3 : 10

[B].

10 : 11 : 20

[C].

23 : 33 : 60

[D].

Cannot be determined

Answer: Option C

Explanation:

Let A = 2k, B = 3k and C = 5k.

A’s new salary = 115 of 2k = 115 x 2k = 23k
100 100 10
B’s new salary = 110 of 3k = 110 x 3k = 33k
100 100 10
C’s new salary = 120 of 5k = 120 x 5k = 6k
100 100
New ratio 23k : 33k : 6k = 23 : 33 : 60
10 10

A bag contains 50 paise, 1 rupee and 2 rupee coins in the ratio 2:5:8. If the total amount is Rs. 352, find the total number of coins in the bag.

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A bag contains 50 paise, 1 rupee and 2 rupee coins in the ratio 2:5:8. If the total amount is Rs. 352, find the total number of coins in the bag.

A. 160
B. 200
C. 250
D. 240
Let the number of 50p, 1 rupee and 2 rupee coins be 2x,5x and 8x. 0.5*(2x)+5x+2*8x = 352 22x=352 x=16 Total no. of coins
= 2x+5x+8x
= 15x = 240

Three quantities X, Y and Z are such that XY=kZ where k is constant. Initially, X was at 4 and X:Y:Z was 2:3:4. If the value of Y is changed to 12 and Z is kept constant, find the value of X.

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Three quantities X, Y and Z are such that XY=kZ where k is constant. Initially, X was at 4 and X:Y:Z was 2:3:4. If the value of Y is changed to 12 and Z is kept constant, find the value of X.

A. 2
B. 3
C. 5
D. 6
X:Y:Z=2:3:4
X=4
Then, Y=6, Z=8 XY=kZ 4*6=k*8 8k=24 k=3
Y=12, Z=8
X*12=3*8
X=2