Ratio and Proportion

WhatsApp D. Pharma Group Join Now
Telegram D. Pharma Group Join Now
Telegram Group Latest Pharma Jobs Join Now
Telegram B. Pharma Group Join Now
Telegram Medicine Update Group Join Now
WhatsApp B. Pharma/ GPAT Channel Join Now
Spread the love

1. (d); Let present ages of Ramu and Somu be R and S respectively.
7R – 6S = 1 …..(i)

8R – 7S = – 4 ….(ii)

Multiplying equation (i) by 8 and equation (ii) by 7, We get 

56R – 48S = 8 ….(iii)

56R – 49S = – 28 ….(iv)

Subtract (iv) from (iii): S =36years

Shortcut:

One year ago → R:S ⇔ 6:7 ⇒S=7

Only option (d) has a number from which, if we subtract ‘1’, we get a number divisible by 7.

2. (b); 33% of A = 33 × A/ 100 =  55× B/100 = 55% of B

= 33 × A/100 = 55 × B/ 100⇒ A/B = 55/33

A:B⇔ 5:3

3. (a); 68% of two fifth of 550

= 68(2/5 * 550)/100 = 68*220/100 = 748/5 =149.6

4. (c); Let, number is ‘n’

(45n/100 )-24=48⇒ 9n/20 – 24 = 48

9n-480=48*20⇒ 9n = 960 + 480

n= 1440/9 =160⇒ 3/8 * n = 3/8 * 160 = 60

5. (a); 30% of the number = 190.8

1% of that number = 190.8/30

175% of the number = 1908/300 × 175=159×7 =1,113 

6. (c); 3/8 * 1000 =375⇒ 32% of (3/8th of 1000) = 32% of 375 = (32 * 375)/100 = 120

7. (c); Let the third number be n.
20% more than n = n + n/5 = (6n)/5

50% more than n = n + n/2 = (3n)/2

Ration of (6n)/5 and (3n)/2 = 6n/5 × 2/3n = 4:5

Shortcut
Let the third number be 100.

Then the two numbers are,

20% more and 50% more

⇓                         ⇓
120                     150

Ratio 120:150=4:5

8. (c); A: B: C:D⇒ 5:2:4:3

⇒ C gets 1 unit more than D.
Given, C gets Rs. 1000 more than D.
⇒1 unit = Rs, 1000 ⇒B’s share = 2 units

= 2 * 1000 = Rs. 2000

9. (b); 0.75:x::5:8

0.75/x = 5/8⇒ 5x = 6.00⇒ x=1.2

Shortcut

0.75:x::5:8 ⇒ 0.75 → 5 ⇒ 1 →0.15 ⇒8→1.20

10. (b); Three numbers = I, II, III

I + II + III = 98, I : II → 2:3, II: III → 5:8

10:15 ⇐ (2:3) × 5 ← (I : II) × 5

15:24 ⇐ (5:8) × 3 ← (II : III) × 3

I: II: III, 10:15:24, 10 + 15 + 24 = 49

Given I + II + III = 98, 98/49 = 2

⇒ 1 unit = 2

⇒ Second number = 15 × 2 = 30

11. (b); A : B = 5 :7

B: C = 6:11

So, we have to quantity B which to be equal in both case.
So, A : B = [5 : 7] * 6

B : C = [6: 11] * 7

So, A : B : C =  30: 42 : 77

12. (d); Let A =2x, B = 3x and C = 4x

So, A/B = (2x)/(3x), BC = (3x)/(4x) and C/A = (4x)/(2x)

⇒ A/B: B/C: C/A = 2/3:3/4:4/2 = 8:9:24

13. (b); 435/25= 2(2×2.35)/25 =27/25 = 4/1

14. (a); x/y = 2/1, x2/y2 =4/1

⇒ (x2+ y2)/(x2-x2) = (4 + 1)/(4 – 1)

(x2-y2)/(x2+y2) = 3/5

15. (c); 19(4x2 – 3y2) = 12(2x2 + 5y2)

52x2 =117y2 ⇒ 4x2= 9y2

x/y = 3/2

16. (a); Let (a + b) = 6k, (b + c) = 7k and (c + a) = 8k then, 2(a + b + c) = 21k

2*14=21k⇒ k = 4/3

So, (a + b) = 6 * 4/3 = 8

c = (a + b + c) – (a + b) = 14 – 8 = 6

17. (d); Given ratio = 1/2:2/3:3/4 = 6:8:9

So, Ist part is = 6/23 × 782 = 204 

18. (d); Let the original salaries of Ravi and Sumit be 2x and 3x.

Then, (2x + 4000)/(3x + 4000) = 40/57

3x = 34000

Sumit’s present salary = (3x+4000) = 38000

19. (b); A = 2/3 * B,      B = 1/4 * C

So, A : B : C = 2 : 3 : 12

A’s share = 2/17 × 510 = 60

B’s share = 3/17 x 510 = 90

C’s share = 12/ 17 x 510 = 360

20. (c); Let Boys = 3x and girls = 2x

No. of students who do not get scholarship = (80% of  3x) + (75%  of  2x) = 39x/10

Req. percentage = (39x/10 × 1/5x × 100)% = 78%

21. (b); 10% of B = 1/4 ×G

B/G = 5/2

22. (b); Let fixed amount = x

Cast of each unit = y

540y + x = 1800

620y + x = 2040

from (i) and (ii)

x = 180,  y = 3

So, total charges for consuming 500 units = (180 + 500 * 3) = 1680

23. (b); Let C gets Rs. x and B gets Rs. (x + 8)

A gets Rs. (x + 15)

So, Sum of A + B + C = 53

x + x + 8 + x + 15 = 53

x = 10

So, A: B: C = 25 : 18: 10

24. (c); Let the no. of 25p, 10p and 5p coins be x, 2x and 3x respectively.

So, Sum of their values = (25x/100 + (10 * 2x)/100 + (5 * 3x)/100) = 60x/100  = 30

So, x = 50

So, the no. of 5p coins = 3 x 50 = 150

Shortcut:

                          25p      10P        5P

No. of coins      1      :   2      :     3 

=300/6

So, No. of 5p coins = 50 × 3 = 150 coins

25. (b); From the question

50 * 2K + 100 * 3K + 500 * 4K + 1000 * K = 34000

K = 10

So, No. of 500 notes = 4 × 10 = 40

26. (a); From the Question C/(A + B) = 3/4,        B/(A + C) = 12/23

So, the sum of both term of the ratio C + A + B = 3 + 4 = 7

So, runs scored by C= 3/7 × 1750 = 750 runs

Similarly,

runs scored by B = 12/ 12+23 × 1750 = 600 runs

and runs scored by A = 1750 – 750 – 600 = 400run

27. (c); No. of employees in class – 1 = 5/17 * 68 = 20

No. of employees in class – 2 = 10/17 * 68 = 40

No. of employees in class – 3 = 2/17 * 68 = 8

So, Salary of each class employee be 2x, 3x and 5x.

So, 20 * 2x + 40 * 3x + 8 * 5x = 400000

x = 2000

So, salary of employee of class – 3 is = 10000

28. (a); According to the Question 20 * 2x + 40 * 3x + 8 * 5x = 400

x = 2

So, he spent 20 * 2 * 2,     40 * 3 * 2,      8 * 5 * 2 on those three vehicles respectively.

So, the spent on car = 240

29. (a); Price (weight)²

P W2

P = K * (10x)2  ………… (i)

Now, total price of broken pieces of diamond Pn = K[x2 + (2x)2 + (3x) 2 + (4x)2] = 30K * x2 ……….(ii)

A.T.Q.

P – Pn = 2, 10,000

K * 100x2 – K * 30x2 = 2, 10,000

70K * x2 = 2, 10,000

Price of unbroken diamond = 100K * x2 = 3 ,00,000

30. (a); (a + b)/5 = (b + c)/6 = (c + a)/7 = (a + b + b + c + c + a)/(5 + 6 + 7)

= 2(a + b + c)/18

a + b = 5x,    a + b + c = 9x,   b + c = 6x and c + a = 7x

Now, a + b + c = 18

So, the value of x = 18/9 = 2

So, b = 2 * 2 = 4

31. (a); 2a = 3b

a/b = 3/2,       b/c = 4/3

So, a:b:c = 6:4:3

32. (a); The ratio of 1 rupees: 50 paise: : 25 paise = 5/6 × 3/ 5 : 3/5 :1 

= 5:6:10

From the Question

5K + 50/100 * 6K + 25/100 * 10K = 262.5

K = 25

So, the no. of 25 paise coin is = 250

33. (a); male amount/ female amount = 4/3  and female amount/ children account = 6/5

So, ratio of male amount: female amount: children = 8:6:5

from the question,

10 * 8K + 15 * 6K + 5 * 5K = 11700

K = 60

So, each child get = 300

34. (a); From the question

(5x – 2500)/(4x – 2500) = 10/7

x = 1500

Shyam’s income = 4 × 1500 = 6000

35. (a); 1 cows = 3 calves

The ratio of the cattles of A, B and C.

= 4×3+3:5×3+4:6×3+5 = 15: 19: 23

Ratio of rents = 15×5:19 × 3:23 × 2 = 75: 57: 46

Rent of B = 2670 * 57/ 75 + 57 + 46 = 855

The difference between rent of A and C = (75 – 46)/(75 + 57 + 46) * 2670 = 435

36. (a); The ratio of capitals of OM, Jai, Jagdish

= 5000 × 12:3000×4+4000×8:7000×8+3000 × 4 =  15: 11: 17

So, Jagdish’s share = 17/43 × 34400 = 13600

37. (b); Let Ram, Krishna and Ganesh invested 5x, 4x and 3x.

Ram’s Capital = 5x * 3 + 3x * 6 = 33x

Krishna’s Capital = 4x * 4 + 3x * 5 = 31x

Ganesh’s Capital  = 3x * 4 + 4x * 5 = 32x

 So, clearly shows Max. profit gained by Ram.

Ram’s profit = 33/96 × 19200 = 6600

38. (c); The amount given to B as management fees = 12%  of 7500 = 900

the rest amount of profit = 7500 – 900 = 6600

Ratio of capitals of A and B = 12000/ 14400 = 5/6

A’s share = 5/ 5+6 × 6600 = 3000

B’s share = 7500-3000 = 4500

So, Difference between A and B share is = 1500 

39. (a); Let the capital of Laxmi and Saraswati be 7x and 5x.

Let, Saraswati’s capital was invested for y months.

So, the ratio of their capital = 7x × 20 : 5x × y

140x/ 5xy = 4/3 ,   y = 21 months

40. (c); p/q = r/s = t/u = 2/3 ⇒ mp/mq = nr/ns = ot/ou = 2/3

⇒ (mp + nr + ot)/(mq + ns + ou) = (2 + 2 + 2)/(3 + 3 + 3) = 2/3

41. (a); √2 / (1+√3) = 6/ x 

x = √3 (1+√3)  = 3 + √3

42. (d); Ratio of Vinay and Aditya for one month

= (50000 × 12) + (80000 × 24): (70000 × 24)

= 600000 + 1920000 : 1680000 = 3:2

Hence, share of Aditya in the profit earned from the business = 87500/ (3+2) x 2 = 35000

33. (b); Let the score of Ajay = x

Rahul = x-15

Manish = x – 25

As per the question

x = 63 + 30 = 93

score of Ajay = 93

Rahul = 93-15 = 78

Manish = 93-25 = 68

Total marks of Rahul, Manish and Suresh = 3 * 63 = 189

Suresh = 189 –  (78 + 68) = 43

Manish + Suresh = 68 + 43 =111

44. (d); Let A’s amount be 5x

B’s amount be 6x

Again let B invested the capital for y months.

5x × 8/ 6x × y = 5/9 ⇒ 40/ 6y = 5/ 9

y = 9 × 40/ 6 × 5 = 12 months 

45. (d); Ratio of profit among A, B and C

= (42000 × 4 +30000 × 6) : (30000 × 4 + 24000 × 6) : (28000 × 4 + 20000 × 6)

= 348 : 264 : 232

Hence C’s share = (46420/844) × 232 = 12760

46. (c); Difference of amount received by R and Q is (7 -5) = 2

Total amount received P and Q = (3 + 5) = 8.

Then, 2 corresponds to 4000 implies that 8 corresponds to (4000/ 2) × 8 = 16000

47. (d); 1213

48. (a); Total of max. marks of all subjects = 105 × 5 = 525

80% of 525 = (525 × 80)/ 100 = 420

Obtained marks of 4 subjects = 360

So, marks obtained in science = 420-360 = 60

49. (c); There are 70 males out of 120 applicants, there must be 50 females.

Thus, no. of males having a drives’s licence all 50 females must having a drives’s licencse will be 80-50 = 30. The max. possible no. of males having a driving license is 70.

So, ratio between the min. and max. is 30:70 or 3 :7.

50. (b); Given ratio of employees = 9:13:18

A.T.Q.

18x = 54

x = 3

No. of employees of type A = 9 × 3 = 27

Similarly, wages of every employee of type A = (10/7) × 1400 = 2000

Req. wages = 27 × 2000 = 54000


Spread the love
Dhalendra Kothale

Dhalendra Kothale

Leave a Reply

Your email address will not be published. Required fields are marked *

Back to top

This will close in 0 seconds

Registration Form


This will close in 0 seconds

WhatsApp Join Telegram