Question 1

The ratio between the number of sheep and the number of horses at the Stewar farm is 4 to 15. If each of horse is fed 110 ounces of horse food per day and the farm needs a total 13200 ounces of horse food per day. what is number sheep in the form ?

Accepted Answer

Given ratio of number of sheep and horses = 4 : 15 Let number of sheep and horses are 4k and 15k Number of horses = 13200/110 = 120 Now 15K = 120 and k = 8 Number of sheep = 4k = (4 x 8) = 32

Question 2

On her deathbed, a grand mother called upon his three grand sons and told them to distribute all her assets worth Rs. 52,500 in the ratio of 1/35 : 1/21 : 1/15 amongst themselves. Find the smallest share amongst the three portions ?

Accepted Answer

The ratio of distribution should be: 21 x 15 : 15 x 35 : 35 x 21 = 315 : 525 : 735 = 3 : 5 : 7 The smallest share will be of worth: 3/15 x 52,500 = Rs. 10,500

Question 3

A Product is supported each week by the same three Product supporters. Last month the first supporter took 440 calls, the second took 360 calls, and the third took 300 calls. This month the job will consists of 1500 calls. If the three supporters ea…

Accepted Answer

1st supporter recieve 440 calls 2nd supporter recieve 360 calls 3rd supporter recieve 300 calls So total calls = 1100 calls ; Calls this month= 1500 So remaining calls to be distributed is 400 So Now Ratio 1st:2nd:3rd ==> 440:360:300 => 22:18:15 Now No. of More Calls 2nd supporter will get => [18/(22+18+15)] x 400 => (18/55) x 400 => 131 Calls So 131 more Calls than last month.

Question 4

Rs. 7444 is divided among 5 ladies, 3 gents and 3 girls. The ratio of share of a lady, a gents and a girl is 7: 4: 3. What is the share of gents ?

Accepted Answer

Ratio of the share of a lady, a gents and a girl is 7 : 4 : 3 No of ladies, gents and girls are 5, 3, 3 Thus effective ratio of ladies, gents and girls is 7 x 5 : 4 x 3 : 3 x 3 = 35 : 12 : 9 so part of gents = (12/56) x 7444 = Rs. 1595.142 so part of 1 gents = 1595.142/3 = Rs. 531.71.

Question 5

A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions made by the larger wheel is ?

Accepted Answer

Here the number of cogs is inveresly proportional to number of revolutions => More cogs less revolution => 6 : 14 :: x : 21 => (21x6)/14 = 9

Question 6

The incomes of two persons A and B are in the ratio 3:4. If each saves Rs.100 per month, the ratio of their expenditures is 1:2. Find their incomes ?

Accepted Answer

The incomes of A and B be 3P and 4P. Expenditures = Income - Savings (3P - 100) and (4P - 100) The ratio of their expenditure = 1:2 (3P - 100):(4P - 100) = 1:2 2P = 100 => P = 50 Their incomes = 150, 200

Question 7

If y/(x - z) = (y + x)/z = x/y then find z : y : x ?

Accepted Answer

Given, y/(x - z) = (y + x)/z = x/y y z = x y + x 2 - y z - x z . . . . ( 1 ) Also x y = y x - z ⇒ x 2 - x z = y 2 . . . . ( 2 ) Using (1) and (2), we get yz = xy - yz + y 2 2yz = xy + y 2 2z = x + y Only option (B) satisfies the equation.

Question 8

At the university entrance exam, a candidate is admitted according to whether he has passed or failed the test. Of the candidates who are really capable, 80 % pass the test and of the incapable, 30 % pass the test. Given that 40 % of the candidates …

Accepted Answer

If there are total 100 candidates, 40 candidates are really capable and 60 candidates are incapable. Of the candidates who are really capable = 80% 40*(80/100)=32 pass the test and of the incapable= 30% 60*(30/100)=18 pass the test. Total candidates who passed the test = 32+18 = 50 The proportion of the really capable students who can pass the test to the total students who can pass = 32/50 = 16/25.

Question 9

Rajitha invested 25% more than Santhosh. Santhosh invested 30% less than Raju, who invested Rs. 6,000. What is the ratio of the amount that Rajitha invested to the total amount invested by all of them together ?

Accepted Answer

Santhosh's investment = 6000 x 70/100 = Rs.4200 Rajitha's investment = 4200 x 5/4 = Rs.5250 Therefore, total amount invested = 6000 + 4200 + 5250 = Rs.15450. Required ratio = 5250 : 15450 = 35 : 103.

Question 10

6 pumps of kirlosker can fill a tank in 7 days and 2 similar pumps of USHA can fill the same tank in 18 days. what is the ratio of the efficiency of a kirlosker pump and a USHA pump?

Accepted Answer

The number of days required by a single kirlosker pump to fill the tank = 6 x 7 =42 days and the number of days required by a single USHA pump to fill the same tank = 2 x 18 =36 days. Now , since efficiency is inversely proportional to the number of days. Hence, E f f i c i e n c y o f o n e K - p u m p E f f i c i e n c y o f U - p u m p = 36 42 = 6 7

Question 11

If (2a + 3b)/(5a - 3b) = 23/5 , then the value of ba is ?

Accepted Answer

Given (2a + 3b)/(5a - 3b) = 23/5 => 10a + 15b = 115a - 69b => 105a = 84b => 5a = 4b a/b = 4/5 => a=4 & b=5 => bxa = 5x4 = 20.

Question 12

Which of the following could not be the lengths of the sides of a right angled triangle?

Accepted Answer

Using Pythagoras theorem we can see that 122 + 152 is not equal to 182 Neither is 102 + 242 = 252

Question 13

There are 209 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 11 : 8, then how many nurses are there in the hospital?

Accepted Answer

Given, The ratio of the doctors to the nurses is 11 : 8 Number of nurses = 8/19 x 209 = 88.

Ratio and Proportion Questions