Ratio and Proportion For SBI PO : Set – 03

1) A box containing Rs.200 consists of one rupee,50 paise,25 paise coins in the ratio of 3:4:5.Find the number of 50 paise  coins?

a) 128

b) 145

c) 162

d) 136

e) None of these

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a)

Value of 1 Rs coin: value of 50 paise coins: value of 25 paise coins

Therefore value of 50 paise coins = {8}/{12+8+5}*200

x=64

Number of 50 paise coins=64x2

=128

2) A factory employs skilled workers, unskilled workers and clerks in the proportion 8 : 5 : 1 and the wages of a skilled worker as unskilled worker and a clerk are in the ratio 5 : 2 : 3. When 20 unskilled workers are employed, the total daily wages of all, amount to Rs. 318. Find the daily wages paid to each category of employees (Rs. ) :

a) 240, 57, 19

b) 210, 70, 13

c) 230, 65, 12

d) 210,70,15

e) 240,60,18

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e)

No. of employees in the ratio = 8: 5: 1

Their wages = 5: 2:3

Their cumulative salary = 40: 10: 3

Daily wage of clerk = {3/53}* 318 = 18

Daily wage of skilled worker = {40/53}* 318 = 240

Daily wage of unskilled worker = = {10/53}* 318 =60

3) The total salary of A, B and C is Rs. 906. If they spend80%, 85%, 75% of their salaries respectively, their savings are as 7 :6 :19. Then salary of B is:

a) Rs 140

b) Rs 160

c) Rs 144

d) Rs 225

e) Rs. 240

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e)

They spend 80% , 85%, 75% of their salary.

So, they save 20%, 15%, 25% and savings are in  the ratio 7 : 6 : 19

20% of x  = 7a

x= 35 a

Similarly, 15% of y = 6a

y = 40a

Similarly, 25% of z = 19 a

Z= 76a

Then the salary of B =  {401/151a}*  906

= Rs. 240

4) There are 43800 students in 4 schools of a city. If half of the first , two-third of the second, three-fourth of the third and four-fifth of the fourth are the same number of students, then find the ratio of number of students of A and D if A, B, C and D be the first, second, third and fourth schools respectively.

a) 5 : 9

b) 7: 6

c) 9: 7

d) 8: 5

e) 9: 5

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d)

A/2:2B/3:3C/4:4D/5

A: B = 4 : 3

B: C = 9: 8

C: D = 16: 15

A : B : C : D = ( 4 x 9 x 16) : ( 3 x 9 x 16 ) : ( 3 x 8 x 16 ) : ( 3 x 8 x 15 )

A: D = 576: 360

A: D = 8: 5

5) Rs 900 were divided among A,B and C in such a way that A had Rs.60 more than B and C had Rs. 30 more than A. How much was C’s Share?

a) Rs 270

b) Rs 340

c) Rs 135

d) Rs 235

e) None of the above

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b)

Let B have x Rs with him

Then A has = (60+x)

Then C has = (30+A) = (30+60+x) = 90+x

Hence A+B+C = 900

60+x+x+90+x = 900

3x+150 = 900

3x = 750

x = 250 Rs

Then C gets 90+x = 90+250 = 340 Rs

6) The ratio of the present ages of a sankar and kumar is 1 : 5 and that of his friends maha and kumar is 4:5. After 2 years the ratio of the ages of the sankar to that of his friend maha becomes 3:10. What is the present age of the kumar?

a) 37 years

b) 35 years

c) 44 years

d) 39 years

e) None of these

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b)

let the present age of the sankar be x years

present age of the kumar = 5 x

present age of the maha = 4x

after 2 years ,

age of the sankar = x + 2

age of the maha = 4x + 2

according to the question , x+2/4x+2=3/10

10(x+2)= 3(4x+2)

10x+20=12x+6

2x=14

x=7

5x=5*7=35

present age of the kumar = 35 years

7) A and B started a partnership business investing capital in the ratio of 3 : 5. C joined in the partnership after six months with an amount equal to that of B. At the end of one year, the profit should be distributed among A, B and C in — proportion.

a) 10 : 5 : 4         

b) 5:3:4

c) 3:4:5

d) 6 : 10 : 5

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d)

 Initial investment capital ratio of A and B = 3 : 5

Hence we can assume that initial capital of A and B are 3x and 5x respectively.

Amount that C invest after 6 months = 5x (Since it is equal to B’s investment)

Ratio in which profit should be distributed after 1 year = 3x*12 : 5x * 12 : 5x*6

=> 3*12 : 5*12 : 5*6

= 6 : 10 : 5

8) Present ages of Kiran and Syam are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Syam’s present age in years?

a) 28

b) 27

c) 26

d) 24

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d)

Ratio of the present age of Kiran and Syam =5:4

Let present age of Kiran =5x

Present age of Syam =4x

After 3 years, ratio of their ages =11:9

⇒ (5x+3): (4x+3) =11:9

⇒ 9(5x+3) = 11(4x+3)

⇒45x+27 = 44x+33

⇒x = 33−27 = 6

Syam’s present age = 4x = 4×6 = 24

9) A policeman starts to chase a thief and moves 8 steps when the thief takes 10 steps, but 7 steps of the thief equals 5 steps of the policeman. The ratio of the speeds of the policeman and the thief is,

a) 25 : 28   

b) 26 : 25   

c) 25 : 26   

d) 28 : 25

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d)

5 Steps of Policeman = 7 steps of thief

1 step of Policeman = 7/5  steps of thief

8 step of Policeman = 8*7/5 steps of thief

= 56/5  Steps of thief

Ratio of speed Policeman  &  thief = Ratio of distance covered by policeman  &  thief in same time = {56/5}:1= 56:5 = 28: 25

10) If two numbers are in the ratio 7:12 and their least common multiple is 336 , what is the sum of the numbers?

a) 57

b) 67

c) 75

d) 76

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d)

Let two numbers 7x,12x

Their LCM=84x=336

X=336/84=4

Therefore two numbers=7*412*4

Therefore sum=28+48=76

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