Test: Ratio and Proportion- 2 - Railways MCQ

To find the total amount of money divided between P, Q, and R in the ratio of 3:7:12:
Given:

• Let k be the common multiplier.
• P's share = 3k
• Q's share = 7k
• R's share = 12k

Equations:

1. Difference between Q and P:
   7k - 3k = 4k = X
2. Difference between Q and R:
   12k - 7k = 5k = 3000

Solve for k:
k = 3000 / 5 = 600

Calculate Shares:

• P's share = 3k = 1800
• Q's share = 7k = 4200
• R's share = 12k = 7200

Total Amount:
Total = 1800 + 4200 + 7200 = 13200

• A= (2/3) x B; B= (1/3) x C;
• Therefore , A/B = 2/3 and B/C = 1/3
• A:B = 2:3 ; B:C = 1:3;
• A:B:C = 2:3:9
• C = 9/14 x 1638 = 1053

• Ans– C 
• For solving this question we need to use a hit and trial method 
• As we approached option c, X = 40; Z = 75
•  Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x)
• i.e., (140/100 * 5x), (150/100 * 7x) and (175/100 * 8x)
• i.e., 7x, 21x/2 and 14x
• Required ratio = 7x : 21x/2 : 14x
• = 14x : 21x : 28x
• = 2 : 3 : 4

The given ratio is:
A : B : C = 3 : 5 : 7
Let the common factor be x. Thus, the production units will be:
A = 3x
B = 5x
C = 7x
We are also given that the total production is 30,000 units. So:
3x + 5x + 7x = 30,000
15x = 30,000
x = 2,000
Now, substitute x = 2,000 into the expressions for each product:
A's production = 3 × 2,000 = 6,000 units
B's production = 5 × 2,000 = 10,000 units
C's production = 7 × 2,000 = 14,000 units
So, the production for A, B, and C is:
A = 6,000 units
B = 10,000 units
C = 14,000 units

Final Answer:
Initial production:
A = 6,000 units, B = 10,000 units, C = 14,000 units

Answer – C.A = 1767; X = 2945
Explanation : 4/15 * A = 2/5 * B
A= 3/2 B;
A:B = 3:2;
check which option have 3:5 with X
A = 3/5 X
A = 3/5 x 2945
A = 1767
 

Answer – C.40
Explanation : x+y=100 ————– (i)
44.50x + 55.25y = 4880 ————– (ii)
Solving (i) and (ii) Y = 40

4x – 2y = 5000 and 5x – 3y = 5000.
X = 2500, so income = 10000 and 12500.

Answer – D.Sum = 98; B = 30 Explanation : A:B:C = 10:15:24
If sum = 98, B = 15/49 * 98 = 30

• Let the number of boys = 3x and the number of girls = 2x.
• After adding 10 girls, the new ratio becomes:
• 3x/(2x + 10) = 3/4
• Cross-multiply:
• 4 × 3x = 3 × (2x + 10)
• 12x - 6x = 30
• 6x = 30
• x = 5
• No of boys = 5x = 5 * 5 = 25 boys

Answer – c) 100:161
Explanation : Boys = 4x and girls = 7x
Ratio = 4x*125/100 : 7x*115/100
= 100:161

Answer – b) 1:2
Explanation :
(40/100)*a + b = (120/100)*b
a:b = 1:2

• We use the allegation method here.
• Zinc content in the first alloy: 5/8
• Zinc content in the second alloy: 7/16
• Desired ratio of zinc to copper: 3/5
• Using the allegation method:
• 5/8 − 3/5 : 3/5 − 7/16
• Simplify:
• (25 − 24)/40 = 1/40
• (48 − 35)/80 = 13/80
• Therefore, the required ratio is:
• 2:13

• Let height of both candles is ‘h’
• let after t times ratio between the height be h – t*(h/6) : h – t*(h/4) = 2:1
• On solvoong we get
• t = 3 hour

• Answer – b) decreases 21:20
• Explanation :
• Let initial employees be 7x and then 4x
• similarly initial wages be 3y and then 5y
• so total wage = 21xy initially and then 20xy
• so wages decreases and ratio = 21:20

• Answer – b) 32
• Explanation :
• milk = 4x and water = 3x
• milk = 4x – 14*4/7 and water = 3x – 14*3/7 + 14
• 4x – 8: 3x + 8 = 3:4
• X = 8,
• so milk = 8*4 = 32 litres

• Answer – b) 10.5
• Explanation :
• (3x – 3)/(4x – 3) = 1/2
• x = 1.5
• sum of the numbers = 3x + 4x = 7x = 7 * 1.5 = 10.5

Answer – c) 42
Explanation :

• a: b = 2:3 and b:c = 4:5
• a:b:c = 8:12:15
• Difference between first and third number  = (7/35)*210 = 42

• The correct option is D 20
• Let number of 25 paise coins be x and 50 paise be y.
• x + y = 70…(i)
  25x + 50y = 3000…(ii)
• On multiplying (i) by 25 and (ii) by 1, we get
• 25x + 25y = 1750
  25x + 50y = 3000
  (i) - (ii) ⇒
• − 25y = − 1250
• or y=125025=50
• On substituting value of y in (i)
• x + 50 = 70
• or x = 70 – 50 = 20

  ∴ Number of 25 paise coins is 20 and 50 paise coins is 50.

Answer – b) 4000, 5000
Explanation :

• 4x – 2y = 2000 and 5x – 3y = 2000.
• On solving both the equations, we get
• x = 1000,
• so income =4x and 5x =  4000 and 5000