Top 50 Aptitude Question asked in SRM PLACEMENTS

Ratio and Proportion

1. Present age of Vinod and Ashok are in ratio of 3:4 respectively. After 5 years, the ratio of their ages becomes 7:9 respectively. What is Ashok's present age is ?

Question 1 Explanation: 

Let the present age of Vinod and Ashok be 3x years and 4x years respectively.

Then (3x+5) / (4x+5)  = 7 / 9

∴ 9(3x + 5) = 7(4x + 5)

∴ 27x + 45 = 28x + 35

∴ x = 10

∴ Ashok's present age = 4x = 40 years

2. At present, the ratio between ages of Ram and Shyam is 6:5 respectively. After 7 years, Shyam's age will be 32 years. What is the present age of Ram?

Question 2 Explanation: 

Let the present age of Ram and Shyam be 6x years and 5x years respectively.

Then 5x + 7 = 32

∴      5x = 25

∴        x = 5

∴ Present age of Ram = 6x = 30 years

3. The present ages of A, B and C are in proportions 4:5:9. Nine years ago, sum of their ages was 45 years. Find their present ages in years

Question 3 Explanation: 

Let the current ages of A, B and C be ax years, 5x years and 9x respectively.

Then (4x-9) + (5x-9) + (9x-9) =45

∴ 18x – 27 = 45

∴ 18x = 72

∴ x = 4

Present ages of A, B and C are 4x = 16, 5x = 20, 9x = 36 respectively.

4. Two numbers are in the ratio of 2:9. If their H. C. F. is 19, numbers are:

Question 4 Explanation: 

Let the numbers be 2X and 9X

Then their H.C.F. is X, so X = 19

∴ Numbers are (2×19 and 9×19) i.e. 38 and 171

5. In a box, there are 10p, 25p and 50p coins in the ratio 4:9:5 with the total sum of Rs 206. How many coins of each kind does the box have?

Question 5 Explanation: 

Let the number of 10p, 25p, 50p coins be 4x, 9x, 5x respectively. Then, 4x/10 + 9x/4 + 5x/2 = 206 (Since, 10p = Rs 0.1, 25p = Rs 0.25, 50p = Rs 0.5) => 8x + 45x + 50x = 4120 (Multiplying both sides by 20 which is the LCM of 10, 4, 2) => 103x = 4120 => x = 40. Therefore, No. of 10p coins = 4 x 40 = 160 (= Rs 16) No. of 25p coins = 9 x 40 = 360 (= Rs 90) No. of 50p coins = 5 x 40 = 200 (= Rs 100)

6. Mark, Steve and Bill get their salaries in the ratio of 2:3:5. If their salaries are incremented by 15%, 10%, and 20% respectively, the new ratio of their salaries becomes:

Question 6 Explanation: 

Let their old salaries be 2a, 3a, 5a respectively. Then, their new salaries become: 115% of 2a = 2a x 1.15 = 2.3a 110% of 3a = 3a x 1.10 = 3.3a 120% of 5a = 5a x 1.20 = 6a So, the new ratio becomes 2.3a:3.3a:6a Upon simplification, this becomes 23:33:60

7. In a library, the ratio of the books on Computer, Physics and Mathematics is 5:7:8. If the collection of books is increased respectively by 40%, 50% and 75%, find out the new ratio:

Question 7 Explanation: 

40% increase will lead to a factor of 140 and similarly 150 and 175 so new ratio is (5*140):(7*150):(8*175) on solving we get 2:3:4

8. The ratio 5:3 represents 16 liters of a mixture containing milk and water. If 4 liters of water is added and 4 liters of milk is extracted from the mixture, then the ratio of the mixture will be:

Question 8 Explanation: 

Amount of Milk in 16 litres of mixture: (5/8) x 16 = 10 litres Amount of Water in 16 litres of mixture: 16-10 = 6 litres If we add 4 litres of water and extract 4 litres of milk, the total volume remains the same. Amount of Milk in 16 litres of new mixture: = 10 – 4 = 6 litres Amount of Water in 16 litres of new mixture: = 6 + 4 = 10 litres So, the new ratio becomes 3:5.

9. If the ages of Jacob, Max and Samuel are in the proportion 3:5:7 and the average of their ages is 25 years, then find the age of the youngest person.

Question 9 Explanation: 

Let their ages be 3a, 5a and 7a. Then, (3a + 5a + 7a) / 3 = 25 => 15a/3 = 25 => 5a = 25 => a = 5 Therefore, age of the youngest person = 3a = 15 years

10. The ratio of the speed of two trains is 7:8. If the second train covers 400 km in 4 h, find out the speed of the first train.

Question 10 Explanation: 

Let the speed of the two trains be 7x and 8x. Then, 8x = 400 / 4 ⇒ 8x = 100 ⇒ x = 12.5 km/h. Hence, speed of the first train = 7x = 7 × 12.5 = 87.5 km/h.

11. A certain amount of money is distributed between Alfred, Adam, Harry and Leo in the proportion of 5:2:4:3. Harry's share is Rs 1000 more than Leo's share. How much money does Adam get?

Question 11 Explanation: 

Let the shares of Alfred, Adam, Harry and Leo be Rs 5x, Rs 2x, Rs 4x and Rs 3x respectively. Then, 4x – 3x = 1000 ⇒ x = 1000. Therefore, Adam gets = Rs 2x = Rs 2000.

12. If (x:y) = 2:1, then (x²-y²):(x²+y²) = __ ?

Question 12 Explanation: 

Given, x:y = 2:1 ⇒ x²:y² = 4:1. Then, (x²+y²):(x²-y²) = (4+1)/(4-1) [by applying Componendo & Dividendo]. ⇒ (x²-y²):(x²+y²) = 3/5.

13. Syrup and Water are mixed in 2:1 ratio to form 60 litres of a mixture. How much water needs to be added to make the ratio 1:2?

Question 13 Explanation: 

Volume of Syrup in the mixture = 60 × 2/3 = 40 litres. Volume of Water in the mixture = 60 × 1/3 = 20 litres Let the required volume of water be x litres. Then, 40:(20+x) = 1:2 ⇒ 20+x = 80 ⇒ x = 60 litres.

14. Felix and Adam win Rs 1210 together. 4/15 of Felix's share is same as 2/5 of Adam's share. How much did Adam win?

Question 14 Explanation: 

Let Felix's and Adam's share be F and A respectively. Then, 4/15 × F = 2/5 × A ⇒ 20 F = 30 A ⇒ F/A = 3/2 ⇒ F:A = 3:2. Therefore, Adam won = 2/5 of Rs 1210 = Rs 484.

15. Study the given graphs to answer these questions. The total production of wheat is 50 lakh tonnes. Production of wheat in different states of India is given:

Abbreviations : U.P. = Uttar Pradesh, M.P. = Madhya Pradesh, A.P. = Andhra Pradesh, C.G. = ChhattisGarh.
What is the ratio of production by conventional method in A.P. to that by scientific method in U.P.?

Question 15 Explanation: 

The production by conventional method in A.P. = 50*0.22*0.22 = 2.420 lakh tonne The production by scientific method in U.P. = 50*0.13*0.73 = 4.74500 lakh tonne Hence, the required ratio = 2.420 / 4.74500 = 484/949 So, option (A) is correct.

16. In a party, 60% of the invited guests are male and 40% are female. If 80% of the invited guests attended the party and if all the invited female guests attended, what would be the ratio of males to females among the attendees in the party?

Question 16 Explanation: 

Let total males and females be 60x and

40x respectively.

Total number of people = (60x + 40x)

Total number of people who attended :

                 0.8(60x + 40x) = 80x

Let y males attended. It is given all

1females attended

40x + y = 80x

y = 40x which is same as females.

Alternative Approach – Lets total number of people = 100. Therefore, 60 are male and and 40 are female. But total 80 guests are attended and all 40 female attended the party. So, there remaining (80 – 40 = 40) attendees should be male. Then the ration of male to female among attendees is 40 : 40 = 1 : 1

17. In appreciative of social improvement completed in a town, a wealthy philanthropist decided to give gift of Rs. 750 to each male senior citizen and Rs. 1000 for female senior citizens. There are total 300 senior citizens and th 8/9^thof total men and 2/3^rdof total women claimed the gift. What is amount of money philanthropist paid?

Question 17 Explanation: 

Let there be x total men.

Total amount paid = x * 750 * 8/9 + (300 – x)*1000*2/3

                  = x*2000/3 + 300*1000*2/3 – x*2000/3

                  = 200000

18. Details of prices of two items P and Q are presented in the above table. The ratio of cost of item P to cost of item Q is 3:4. Discount is calculated as the difference between the marked price and the selling price. The profit percentage is calculated as the ratio of the difference between selling price and cost, to the cost

Profit% = ((Selling price – Cost)/Cost)×100

The discount on item Q, as a percentage of its marked price, is _______ .

Question 18 Explanation: 

Given, ratio of cost of item P to cost of item Q is 3:4 So, (3/7)*(total cost of P and Q) = 5400 = cost of P Total cost of P and Q = 5400*7/3 = 12600 Hence, cost of Q = 12600*4/7 = 7200 Now, the selling price of Q would be = cost price * (1+profit%) ;as given in table = 7200 * (1+0.25) = 7200*1.25 = 9000 (Discount is calculated as the difference between the marked price and the selling price; as given in table.). Discount % = (MP – SP) / MP = (10000 – 9000) / 10000 = 1000/10000 = 1/10 = 0.1 = 10%

19. The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in Year 3 was Re. 1, which was half the cost/unit in Year 2. The cost/unit in Year 3 was one-third of the cost/unit in Year 1. Taxes were paid on the selling price at 10%, 13%, and 15% respectively for the three years. Net profit is calculated as the difference between the selling price and the sum of cost and taxes paid in that year. The ratio of the selling price in Year 2 to the selling price in Year 3 is _________.

Question 19 Explanation: 

From the above graph we obtained following information- 

Year    Cost/Unit   Cost Price    Number of Units

1             3              300             100

2             2              400             200

3             1              300             300

Let selling price of year 2 = SP2 and Selling price of year3 = SP3

Given that-

Taxes for year 2 = 13% of SP2 = 0.13SP2

Taxes for year 3 = 15% of SP3 = 0.15SP3

Cost per unit of year 3 = 1

(Cost per unit of year 2)/2 = 1

So now Cost / unit of year 2 = 2*1 = 2

Net profit formula now = Selling Price – (Cost Price + (Tax% x selling price )

For year 2

296 = SP2- (200*2 + 0.13*SP2)

SP2 = 696*100/87

SP2 = 800

For year 3

210 = SP3 – (300*1+0.15*SP3)

SP3 = 510*100/85

SP3 = 600

Required Ratio 800/600= 4/3 (Correct Option A)

Mixtures and Alligation

1. There are two types of sugar. One is priced at Rs 62 per kg and the other is priced at Rs 72 per kg. If the two types are mixed together, the price of new mixture will be Rs 64.50 per kg. Find the ratio of the two types of sugar in this new mixture.

Question 1 Explanation: 

Cost Price of 1kg of Type 1 sugar = 6200 p. Cost Price of 1kg of Type 2 sugar = 7200 p. Mean Price of 1 kg of mixture = 6450 p. According to the Rule of Alligation, (Quantity of Cheaper):(Quantity of Dearer) = (CP of dearer – Mean Price):(Mean Price – CP of cheaper) Therefore, the required ratio = (7200-6450):(6450-6200) = 750:250 = 3:1.

2. A certain quantity of water is mixed with milk priced at Rs 12 per litre. The price of mixture is Rs 8 per litre. Find out the ratio of water and milk in the new mixture.

Question 2 Explanation: 

Cost Price of 1 litre of water = Rs 0. Cost Price of 1 litre of milk = Rs 12. Mean Price of Mixture = Rs 8. According to the Rule of Alligation, (Quantity of Cheaper):(Quantity of Dearer) = (CP of dearer – Mean Price):(Mean Price – CP of cheaper) Therefore, Water:Milk = (12-8):(8-0) = 4:8 = 1:2.

3. A drum contains forty liters of whisky. Four liters of whisky is taken out and replaced by soda. This process is carried out twice further. How much whisky is now contained by the container?

Question 3 Explanation: 

Hint: Suppose a solution contains x units of a liquid from which y units are taken out and replaced by water. After n repeated operations, quantity of pure liquid remaining in solution  =x(1−y/x)ⁿ=x(1−y/x)ⁿ units. So, Whisky in the drum now =40(1−4/40)³=40(1−1/10)³ =29.16

4. Rice of rate Rs. 126 per kg and Rs. 135 per kg and 3^rdvariety in the ratio 1 : 1 : 2. If the final mixture is worth Rs. 153 per kg, what is the rate of the third variety per kg?

Question 4 Explanation: 

Rice worth Rs. 126 per kg and Rs. 135 per kg are mixed in the ratio 1 : 1 So their average price =(126+135)/2=130.5 Now there are two mixtures one of rate 130.5 /kg and another is of rate say x /kg 130.5               x 153 x-153              153-130.5   x-153/22.5=1/1 x = 175.50

5. A sikanji vendor has two drums of sikanji. The first contains 75% of sikanji. The second contains 50% sikanji. How much sikanji should he mix from each of the drum so as to get twelve litres of sikanji such that the ratio of sikanji to soda is 5 : 3?

Question 5 Explanation: 

Let x litrs from 1^st drum and 12-x litrs from 2^nd drum are mixed sikanji from 1^st drum = .75x soda from 1^st drum = .25x sikanji from 2^nd drum = .5(12-x) soda from 2^nd drum = .5(12-x) total sikanji = .25x+6 total soda = .25x+.5(12-x) = 6-.25x ratio = (.25x+6)/(6-.25x) = 5/3 .75x+18 = 30-1.25x 2x =12 x=6 sikanji and 6 soda

6. There are two drums of vanaspati gee. One of them contains 25% of oil (and rest 75% gee) and the another contains 50% oil (and rest 50% gee). How much vanaspati gee (approx) should one mix from each of the drum so as to get 14 litres of vanaspati gee such that the ratio of gee to oil is 5 : 2?

Question 6 Explanation: 

Quantity of Ghee in 1st Drum = 75% Quantity of Ghee in 2nd Drum = 50% Total quantity of Ghee required in the final mixture = 14 liters Ratio of Ghee to Oil in the final mixture = 5 : 2 ( i-e 500/7 % Ghee ) By Alligation Rule :

So, we have to mix Ghee from 1st and 2nd Drum in the ratio of 6 : 1 Since total quantity of Ghee in the final mixture is 14 liters. So, Ghee to be mixed from 1st Drum = 6/7*14 = 12 liters. And Ghee to be mixed from 2nd Drum = 1/7*14 = 2 liters.

7. Two solutions S1 and S2 contain whisky and soda in the ratio 2 : 5 and 6 : 7 respectively. In what ratio these solutions be mixed to get a new solution S3,  containing whisky and soda in the ratio 5 : 8 ?

Question 7 Explanation: 

Let the amount taken from S1 be 7xAnd amount taken from S2 be 13y (2x + 6y)/(5x + 7y) = 5/816x + 48y = 25x + 35y9x = 13yx/y = 13/9 Actual ratios of amounts                = 7x/13y               = (7/13) * (13/9)               = 7/9

8. 8 liters of wine is replaced by water from a pot full of wine and repeated this two more times. The ratio of the wine:water left in pot is 8 : 27. 

How much wine was there in the pot originally?

Question 8 Explanation: 

Let initial quantity of wine =x litre 

After a total of 1+2=3 operations, 
quantity of wine 

⇒x(1−y/x)n 
⇒ x(1−8/x)3 
⇒x(1−8/x)3 x = 8/27 
⇒(1−8/x)3 = (2/3)3 
⇒(1−8/x)=2/3 
⇒x=24

9. A vessel full of orange juice contains 40% orange pulp. A part of juice is replaced by another juice containing 19% orange pulp and now the percentage of orange pulp is found to be 26%. What quantity of juice is replaced?

Question 9 Explanation: 

Concentration of orange pulp in 1^st vessel = 40% Concentration of orange pulp in 2^nd vessel = 19% After the mixing, Concentration of orange pulp in the mixture = 26% By rule of alligation,

Hence ratio of 1^st and 2^nd quantities = 7 : 14 = 1 : 2 i.e., 2/(1+2)=2/3 part of the juice is replaced.

10. How many kg of rice, of cost 9 Rs/kg must be mixed with 27 kg of rice of cost 7 Rs/kg get a gain of 10 % by selling the mixture at 9.24 Rs/kg?

Question 10 Explanation: 

Selling Price(SP) of 1 kg mixture= Rs. 9.24 Profit = 10% Cost Price(CP) of 1 kg mixture = 100SP/(100+Profit%) =100*9.24/(100+10) =924/110=8.4 By rule of alligation,

Ratio = 1.4 : 0.6 = 14 : 6 = 7 : 3 Suppose x kg of kind1 rice is mixed with 27 kg of kind2 rice. then x : 27 = 7 : 3 ⇒3x=27×7 ⇒x=9×7=63

11. In what ratio should a kind of sugar at 8.70 Rs/kg be mixed with another kind of sugar at 9.70 Rs/kg so that the mixture be worth 9 Rs/kg?

Question 11 Explanation: 

By rule of allegation,

= 0.7 : 0.3 = 7 : 3

12. In what ratio must rice of one kind worth Rs. 50/kg be mixed with another kind of rice of worth Rs. 55/kg such that by selling the mixture at Rs. 57.20/kg, there can be a gain 10%?

Question 12 Explanation: 

SP of 1 kg mixture = Rs. 57.20 Profit = 10% CP of 1 kg mixture =100SP/(100+Profit%)  =100*57.20/(100+10) =5720/110 =Rs. 52 By rule of allegation  

Hence required ratio = 3 : 2

13. A drum filled with a mixture of two liquids l1 and l2 in the ratio 5:7. When 9 liters of mixture is taken out and the replaced by l1. Now the ratio of l1 and l2 is 9:7. How many liters of the liquid l1 were there in the drum initially?

Question 13 Explanation: 

Let the initial quantity of l1 in the container be 5x. Let the initial quantity of l2 in the container be 7x. Now, 9 liters of mixture is drawn off from the container. Quantity of l1 in 9 liters of the mixture drawn off =9*5/12=15/4 Quantity of l2 in 9 liters of the mixture drawn off =9*7/12=21/4 Hence, Quantity of l1 remaining in the mixture after 9 liters is drawn off =5x−15/4 Quantity of l2 remaining in the mixture after 9 liters is drawn off =7x−21/4 Since the container is filled with l1 after 9 liters of mixture is drawn off, quantity of l1 in the mixture =5x-15/4+9=5x+21/4. Given that the ratio of l1 and l2 becomes 9:7 ⇒5x+21/4:7x-21/4=9:7 ⇒20x+21:28x-21=9:7 ⇒7(20x+21)=9(28x-21) ⇒140x+147=252x-189 ⇒112x=336 ⇒x=3. Therefore, liters of l1 present in the container initially =5x=(5*3)=15.

14. In what ratio a vendor should mix rice at Rs.60 per kg with rice at Rs. 68 per kg so that the final rice mixture must be of worth Rs. 63 per kg?

Question 14 Explanation: 

By rule of alligation,

Required Ratio = 7.5 : 2.5 = 3 : 1

15. A vessel is filled with a solution of, 3 parts soda and 5 parts rum. How much of the solution must be taken out and replaced with soda so that the solution contains equal amount of sod and rum?

Question 15 Explanation: 

Let the total solution = 8 litre. soda in the solution = 3 litre, rum in the solution = 5 litre. Say x Lt of the solution is is taken out and replaced with soda. soda in the new solution =3−(3x/8)+x Quantity of rum in the new mixture =5−(5x/8) soda : rum = 1:1 ⇒3−(3x/8)+x = 5−(5x/8) ⇒x=8/5 if the quantity of the solution is 8 litre, 8/5 litre of the solution needs to be taken out and replaced with soda so that the solution contains equal amount of soda and rum. =>1/5^th of the solution needs to be taken out and replaced with soda so that the solution contains equal amount of soda and rum.