Mathematics

Ratio & Proportion

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Assistant Fire Officer 2022

MEDIUM

In a 40-liter mixture, the ratio of milk and water is 4 : 1. How much water should be added to this mixture so that the ratio of milk and water becomes 2 : 3?

40 L

20 L

48 L

32 L

Explanation

Total 40 L, ratio 4:1. Milk = 32 L, Water = 8 L. Added $x$ water. $32/(8+x) = 2/3 \Rightarrow 96 = 16+2x \Rightarrow 2x = 80 \Rightarrow x = 40$ L.

MEDIUM

Two numbers are in the ratio $2:3$ . If each number is increased by 4, the ratio becomes $5:7$ . The sum of both numbers is-

Explanation

$2x, 3x$ .
$(2x+4)/(3x+4) = 5/7 → 14x+28 = 15x+20 → x=8$ .
Numbers: $16, 24$ . Sum = 40.

MEDIUM

One friend says to another, "If you give me one hundred rupees, I will be twice as rich as you." The second replies, "If you give me ten rupees, I will be six times as rich as you." How many rupees do both have?

140 rupees, 170 rupees

50 rupees, 170 rupees

30 rupees, 170 rupees

40 rupees, 170 rupees

Explanation

Let X = 170, Y = 140.
Let's re-solve the equations:
$Y+100 = 2(X-100) → 2X-Y=300$ .
$X+10 = 6(Y-10) → X-6Y=-70$ .
Multiply second by 2: $2X-12Y=-140$ .
Subtract: $11Y = 440 → Y=40$ .
$X - 240 = -70 → X=170$ .
So 170, 40.

Patwar (Ajmer, Banswara, Barmer) 2011

MEDIUM

The ratio of the ages of Seema and Reema is 9:16. After ten years, the ratio of their ages will be 2:3. What is the difference in their ages in years? [Patwar (Ajmer, Banswara, Barmer) 2011]

16 years

7 years

12 years

14 years

Explanation

Let Seema's age be $9x$ and Reema's $16x$ . $\frac{9x+10}{16x+10} = \frac{2}{3} \Rightarrow 27x+30 = 32x+20 \Rightarrow 5x=10 \Rightarrow x=2$ . Difference in age $16x-9x=7x=14$ years.

पटवार (धौलपुर, जैसलमेर, पाली) - 2011

MEDIUM

A sum of money is divided among A, B, and C in the ratio $2 : 5 : 9$ . If A's share is 2500 rupees, what is the total amount?

18000 Rupees

20000 Rupees

25000 Rupees

22000 Rupees

Explanation

Ratio $2x : 5x : 9x$ .
A's share $= 2x = 2500 \Rightarrow x = 1250$ .
Total amount $= 2x + 5x + 9x = 16x = 16 \times 1250 = 20000$ .

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Patwar (Bhilwara, Dungarpur, Jalore) 2011

MEDIUM

If A:B = 4:5 and B:C = 6:7, then what will be the value of A:C [Patwar (Bhilwara, Dungarpur, Jalore) 2011]

4 : 7

7 : 4

24 : 35

35 : 24

Explanation

$\frac{A}{C} = \frac{A}{B} \times \frac{B}{C} = \frac{4}{5} \times \frac{6}{7} = \frac{24}{35}$ . $A:C = 24:35$ .

Patwar (Alwar, Chittorgarh, Churu) 2011

MEDIUM

What will be the third proportional of 18, 24? [Patwar (Alwar, Chittorgarh, Churu) 2011]

Explanation

Let the third proportional be $x$ . $18:24::24:x \Rightarrow 18x = 24 \times 24 \Rightarrow x = \frac{24 \times 24}{18} = 32$ .

MEDIUM

In a bag, there are 5 rupee, 2 rupee, and 1 rupee coins in the ratio $5:6:7$ . If the total amount is 220 rupees, then the number of 2 rupee coins in the bag is-

120

Explanation

Coins ratio $5x, 6x, 7x$ .
Value: $5(5x) + 2(6x) + 1(7x) = 25x + 12x + 7x = 44x$ .
$44x = 220 → x = 5$ .
2 rupee coins = $6x = 30$ .

MEDIUM

If $(x+5)$ is the mean proportional of two numbers $(x+2)$ and $(x+9)$ , then the value of $x$ is-

Explanation

Mean proportional = $\sqrt{ab}$
$(x+5)^2 = (x+2)(x+9)$
$x^2 + 10x + 25 = x^2 + 11x + 18$
$10x + 25 = 11x + 18 → x = 7$ .

Patwar (Baran, Jodhpur, Pratapgarh) 2011

MEDIUM

If A:B = 7:9 and B:C = 3:5, then what will be the value of A:B:C? [Patwar (Baran, Jodhpur, Pratapgarh) 2011]

9 : 15 : 7

7 : 9 : 15

15 : 9 : 7

9 : 7 : 15

Explanation

$A:B = 7:9, B:C = 3:5$ (multiply by 3) $= 9:15$ . Thus $A:B:C = 7:9:15$ .

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Protection Officer - 28.01.2023

MEDIUM

Copper and Zinc are mixed in ratios 7:3 and 7:5 respectively to form two alloys A and B. If equal quantities of both alloys are melted together to form a third alloy C, then what is the ratio of Copper and Zinc in C? [Protection Officer - 28.01.2023]

49 : 15

35 : 21

77 : 43

63 : 37

Explanation

Explanation - 1 kg quantity of both mixtures has been taken. Copper in new mixture $= \frac{7}{7+3} + \frac{7}{7+5} = \frac{7}{10} + \frac{7}{12} = \frac{42+35}{60} = \frac{77}{60}$ . Zinc in new mixture $= 2 - \frac{77}{60} = \frac{120-77}{60} = \frac{43}{60}$ . Required ratio $= \frac{77}{60} : \frac{43}{60} = 77 : 43$ .

Patwar Exam 2013

MEDIUM

The sum of three numbers is 392. The ratio of the first and second number is 2:3 and the ratio of the second and third number is 5:8. Then the first number is— [Patwar Exam 2013]

100

120

Explanation

Let the numbers be $x, y, z$ . $x:y=2:3, y:z=5:8$ . Thus $x:y:z=10:15:24$ . Total sum $10a+15a+24a=49a=392 \Rightarrow a=8$ . First number $10 \times 8 = 80$ .

पटवार (बीकानेर, हनुमानगढ़, श्रीगंगानगर) - 2011

MEDIUM

In a bag, the coins of 25 paise, 10 paise, and 5 paise are in the ratio $1 : 2 : 3$ . If there are total 30 rupees in the bag, then what is the number of 5 paise coins in it?

50

100

150

200

Explanation

Ratio of coins $= 1x : 2x : 3x$ .
Value: $25(1x) + 10(2x) + 5(3x) = 25x + 20x + 15x = 60x$ paise.
Total value = 30 rupees = 3000 paise.
$60x = 3000 \Rightarrow x = 50$ .
Number of 5 paise coins $= 3x = 3 \times 50 = 150$ .

Patwar Exam 2013

MEDIUM

Determine three such numbers whose ratio is 4:5:6 and the sum of their squares is 1232 [Patwar Exam 2013]

8, 10, 12

12, 15, 18

16, 20, 24

20, 25, 30

Explanation

Let numbers be $4x, 5x, 6x$ . $(4x)^2 + (5x)^2 + (6x)^2 = 1232 \Rightarrow 16x^2 + 25x^2 + 36x^2 = 77x^2 = 1232 \Rightarrow x^2 = 16 \Rightarrow x=4$ . Numbers are $16, 20, 24$ .

पटवार (भीलवाड़ा, डूंगरपुर, जालौर) - 2011

MEDIUM

If $\frac{1}{63} : \frac{1}{21} : \frac{1}{8}$ , then what will be the value?

\frac{1}{6}

\frac{1}{32}

\frac{1}{4}

\frac{1}{24}

Explanation

$\frac{1}{63} : \frac{1}{21} : \frac{1}{8} \Rightarrow \frac{1}{63} : \frac{3}{63} : \frac{1}{8} \Rightarrow \frac{1}{63} : \frac{1}{21} : \frac{1}{8} \Rightarrow \frac{1}{63} \times 504 : \frac{1}{21} \times 504 : \frac{1}{8} \times 504 = 8:24:63$ . (Note: Correct calculation leads to simplified ratio, but checking the answer key: 1/24 implies specific ratio manipulation.)

Patwar 2009

MEDIUM

The ratio of the prices of a scooter and a moped is 7 and 4. If the price of a scooter is ₹3600 more than the price of a moped, then the price of the moped is-

₹4800

₹4600

₹5200

₹4500

Explanation

Price ratio $7x, 4x$ . $7x - 4x = 3600 \Rightarrow 3x = 3600 \Rightarrow x = 1200$ . Price of moped = $4 \times 1200 = 4800$ .

R.A.S. Pre Exam, 28.08.2016

MEDIUM

In a 60-liter mixture, the ratio of milk and water is 5 : 3. If its ratio is to be made 1 : 2, then the amount of water to be added to the mixture will be-

Not Provided

Explanation

Question is incomplete, options are not available.

Patwar (Bhilwara, Dungarpur, Jalore) 2011

MEDIUM

If 4800 Rs are distributed between A, B and C in the ratio 6:5:4, then what is the difference in the shares of A and C? [Patwar (Bhilwara, Dungarpur, Jalore) 2011]

600 rupees

640 rupees

500 rupees

320 rupees

Explanation

Difference = $\frac{6-4}{6+5+4} \times 4800 = \frac{2}{15} \times 4800 = 2 \times 320 = 640$ rupees.

पटवार (झालावाड़, झुंझुनूं, नागौर) - 2011

MEDIUM

What should be added to each term of $7 : 13$ so that the new numbers are in the ratio $2 : 3$ ?

1

2

4

5

Explanation

Let the number be $x$ .
$(7+x) : (13+x) = 2 : 3 \Rightarrow 3(7+x) = 2(13+x) \Rightarrow 21 + 3x = 26 + 2x \Rightarrow x = 5$ .

Patwar (Alwar, Chittorgarh, Churu) 2011

MEDIUM

If 15 percent of m = 20 percent of n, then what will be the value of m:n? [Patwar (Alwar, Chittorgarh, Churu) 2011]

5:4

4:3

17:16

16:17

Explanation

$m \times \frac{15}{100} = n \times \frac{20}{100} \Rightarrow \frac{m}{n} = \frac{20}{15} = \frac{4}{3} \Rightarrow m:n = 4:3$ .

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