**Ratio, Proportion and Variation**

**Ques. 1**** -****If 40 articles cost Rs. 180, the cost of 18 articles is : **

**Ques. 2**** -****A student obtained equal marks in History and Sociology. The ratio of marks in Sociology and Geography is 2: 3 and the ratio of marks in History and Philosophy is 1: 2. If he has scored an aggregate of 55% marks. The maximum marks in each subject is the same. In how many subjects did he score equal to or greater than 60% marks?**

**Ques. 3**** - Four numbers are in proportion. The sum of the ****squares of the four numbers is 50 and the sum of the mean is 5. The ratio of first two terms 1:3. What is the average of the four numbers?**

**Ques. 4**** -****The ratio of income of Anil and Mukesh is 2 : 3. The sum of their expenditure is Rs. 8000 and the amount of savings of Anil is equal to the amount of expenditure of Mukesh. What is the sum of their savings?**

**Ques. 5**** - ****Hutch and Essar entered into a partnership just 5 months ago. The ratio of profit claimed by Hutch and Essar is 6:17. If Essar had just started his business 12 months ago with Rs. 1275, what is the amount contributed by Hutch?**

**Ques. 6**** - A child has three different kinds of chocolates costing Rs. 2, Rs. 5 and Rs. 10. He spends total Rs. 120 on the chocolates. What is the minimum possible number of chocolates, he can buy, if there must be atleast one chocolate of each kind?**

**Ques. 7**** - Mr. Teremere and Mr. Meretere have 5 chocolates and 3 chocolates with them respectively. Meanwhile Mr. Khabbu Singh Joined them and all 8 chocolates were distributed equally among all these three people. In turn Khabbu Singh gave Rs. 16 to Mr. Teremere and Mr. Mereterre, since khabbu Singh did not has any chocolate. What is the difference of amount received by Teremere and Meretere? Given that the amount was shared in proportion of chocolates received by Khabbu Singh.**

**Ques. 8**** - Rs. 4536 is divided among 4 men, 5 women and 2 boys. The ratio of share of a man, a woman and a boy is 7: 4: 3. What is the share of a woman?**

**Ques. 9**** - The concentration of petrol in three different mixtures (petrol and kerosene) is 1/2 , 3/5 and 4/5 respectively. If 2 litres, 3 litres and 1 litre are taken from these three different vessels and mixed. what is the ratio of petrol and kerosene in the new mixture?**

**Ques. 10**** - In a milk shoppe there are three varieties of milk, ‘pure’, ’Cure’ and ‘Lure’ . The ‘Pure’ milk has 100% concentration of milk. The ratio of milk is to water in the ‘Cure’ is 2:5 and in the Lure it is 3:8 respectively. Sonali purchased 14 liters of Cure and 22 litres of Lure milk and mixed them. If she wanted to make the concentration of milk in the mixture of purchased milk to 50% .How many litres of ‘pure’ milk she is needed?**

**Ques. 11**** - In the Squadron of Indian Air Force the ratio of Sukhoi is to Mig and Jaguar together is 5:7 and the ratio of Jaguar is to Sukhoi and Mig together is 1: 2. Find the ratio of Sukhoi and Mig:**

**Ques. 12**** - During our campaign against child labour we have found that in three glass making factories A, B and C there were total 33 children aged below 18 were involved. The ratio of male to female in A, B and C was 4 : 3, 3 : 2 and 5 : 4 respectively. If the no. of female children working in the factories B and C be equal, then find the no. of female children working in factory A?**

**Ques. 13**** - The value of diamond is directly proportional to the square of its weight. A diamond unfortunately breaks into 3 pieces with weights in ratio 3 : 4 : 5, thus a loss of Rs. 9.4 lakh is incurred. What is the actual value of diamond?**

**Ques. 14**** - In Ruchika's wallet there are Rs. 16, consisting of 10 paise, 20 paise and Re. 1 coins. The ratio of number of coins 10 paise coins and 20 paise is 6 : 1. The maximum number of Re. 1 coin is:**

**Ques. 15**** - There are two vessels containing the mixture of milk and water. In the first vessel the water is 2/3 of the milk and in the second vessel water is just 40% of the milk. In what ratio these are required to mix to make 24 litres mixture in which the ratio of water and milk is 1 : 2?**

**Ques. 16**** - The ratio of working efficiency of A and B is 5 : 3 and the ratio of efficiency of B and C is 5 : 8 . Who is the most efficient?**

**Ques. 17**** - Nehru Ji had 'n' chocolates. He distributed them among 4 children in the ratio 1/2 : 1/3 : 1/5 : 1/8. If he gave them each one a complete chocolate, the minimum number of chocolates that he had :**

**Ques. 18**** - If 4A = 5B and 3A = 2C then the ratio of B : C is :**

**Ques. 19**** - Equal quantities of three mixtures of milk and water are mixed in the ratio 1 : 2, 2 : 3 and 3 : 4. The ratio of water and milk in the mixture is ?**

**Ques. 20**** - The ratio of age of A and B is 8 : 9 and the age of B is 2/3 of C's age and age of C is 9/13 times the age of D. If the age of B is 18 years then the age of C is : **

**Ques. 21**** - A milk man has a mixture of milk in which ratio of milk and water is 5 : 3. He sells 40 litres of milk i.e. mixture then he adds up 15 litres of pure water. Now the ratio of milk and water is 5 : 4. What is the new quantity of mixture? **

**Ques. 22**** - A hotel incurs two types of expenses, one which is fixed and others depend upon no. of guests. When there are 10 guests, total expenses of hotel are Rs. 6000. Also when there are 25 guests average expenses per guests are Rs. 360? What is the total expenses of hotel when there are 40 guests?**

**Ques. 23**** - The ratio of third proportional to 21 and 42 and mean proportional to 16 and 49 is ?**

**Ques. 24**** - Rs. 960 were distributed among A, B, C and D in such a way that C and D together gets half of what A and B together gets and C gets one third amount of B. Also D gets 5/3 times as much as C. What is the amount of A?**

**Ques. 25**** - The speeds of rickshaw, car and scooter are in the ratio of 3 : 5 : 6. What is the ratio of time taken by each one of them for the same distance ? **

**Ques. 26**** - Divide Rs. 6940 in such a way that A gets (2/3)rd of what B gets and B gets (3/5)th of what C gets? What is the share of A and B together ?**

**Ques. 27**** - The ratio of age of A and B is x : y. If A's age is increased by 3 years and B's age is increased by 2 years then new ratio of their ages becomes 24: 25. Given that the sum of their actual ages is 93 years. Find the actual ratio of their ages.**

**Ques. 28 -a : b = 4 : 9. If 4 is added to both of the numbers then the new ratio becomes 21 : 46. What is the difference between a and b? **

**Ques. 29**** - The ratio of ages of Rahul and Deepesh is 3 : 5. 10 years later this ratio becomes 5 : 7. What is the present age of Deepesh?**

**Ques. 30 -**** When 5 is added to numerator and denominator both of a (positive) fraction, then the new ratio of numerator to denominator becomes 11 : 15. What is the original ratio ?**

**Ques. 31 -**** Five numbers a, b, c, d and e are in the ratio of 2 : 3 : 5 : 8 : 9 and their sum is 162. Find the average of all these numbers :**

**Ques. 32 -**** 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 ?**

**Ques. 33 -**** 16 persons can reap 1/5th field in 6 days. How many persons (with same efficiency) are required to reap rest of the field in 8 days ?**

**Ques. 34 -**** In a wallet the ratio of 25 paise, 50 paise and Re. 1 coins are in the ratio of 12 : 4 : 3, which amounts to Rs. 600. Find the no. of coins of 25 paise :**

**Ques. 35 -**** Petrol is 7 times heavy than kerosene and castrol Mobil is 18 times as heavy as Kerosene. What should be the ratio of petrol and Mobil in the new mixture to get the mixture which must be 11 times as heavy as kerosene ?**

**Ques. 36 -**** A girl buys 2 pigeons for 182. She sells one at a loss of 5% and another at a profit of 8%. But she neither gains nor loses on the whole. Find the price of pigeon which has sold at a profit.**

**Ques. 37 -**** The ratio of prices of Cello and Rotomac pens in 2000 were in the ratio of 3 : 5. In 2005 the price of Cello pen trebles itself and the price of Rotomac pen is increased by Rs. 100, then the new ratio of prices of the same pens becomes 4 : 5. What was the original price of the Rotomac pen in 2000?**

**Ques. 38 - A rabit takes 22 leaps for every 17 leaps of a cat and 22 leaps of a rabit are equal to 17 leaps of the cat. What is the ratio of the speeds of rabbit and cat ? **

**Ques. 39 -**** 10 years ago the age of Karishma was 1/3rd of the age of Babita. 14 years hence the ratio of ages of Karishma and Babita will be 5 : 9. Find the ratio of their present ages :**

**Ques. 40 -****The ratio of numerator to a denominator of a fraction is 1/5 when x and 5x are added to the numerator and denominator respectively to the given fraction then the ratio of the new fraction will be :**

**Ques. 41 -**** x varies directly as y and x varies indiretly as the square of z. When y = 75 and x = 6, then z = 5. Find the value of x when y = 24 and z = 4.**

**Ques. 42 -**** x varies directly as (y² +z²). At y = 1 and z = 2, the value of x is 15. Find the value of z, when x = 39 and y = 2.**

**Ques. 43 -**** A tin contains a mixture of Dew and Sprite in the ratio of 7 : 3 and another tin contains the Dew and Sprite in the ratio of 5 : 4. In what proportion should the solution of two tins be mixed to achieve a perfect proportion of 2:1 (in which Dew is 2 times that of sprite).**

**Ques. 44 -**** There are two containers A and B filled with mentha oil with different prices and with volumes 140 and 60 liters respectively. Equal quantities are drawn from both A and B in such a manner that the oil drawn from A is poured in into B and oil drawn from B is poured into A. The Price per liter becomes equal in both A and B. How much is drawn from each of A and B :**

**Ques. 45 -**** A three digit number is such that this number itself is divisible by the sum of its digits.The sum of hundreds and unit digit is 6 while the sum of the tens and unit digit is 5. What is the ratio of unit and tens digits :**

**Ques. 46 -**** Sachin bought 1.5 kg fresh grapes. The ratio of water is to pulp was 4:1. When his naughty child crushed these grapes, then some water get wasted. Now the ratio of water is to pulp is 3 : 2. What is the total amount of the crushed grapes?**

**Ques. 47 -**** A man bought 9 mangoes for a rupee and sold them at 6 mangoes for a rupee. What is the ratio of profit to the cost price?**

**Ques. 48 -**** Half of the volume of petrol and kerosene mixture of ratio 7 : 5 is converted into a mixture of ratio 3 : 1 by the substitution (or replacement) method. While the mixture of ratio 7 : 5 was formed from the mixture of 7 : 3 by adding the kerosene in it . If 240 litres petrol is required in the replacement method, what is the total amount of kerosene was added to prepare the mixture of 7 : 5 ?**

**Ques. 49 -****Sometimes ago in a Cinema hall a blockbuster movie was being shown. Due to excessive demand of the show, manager of the cinema hall increased the prices of tickets in all the three categories. 25% in first class, 12.5% in special class and 40% in balcony. If the collection of one show was ₹ 218925, then find the collection from the balcony only given that the ratio of price of ticket (increased price) for first class, special class and balcony is 5: 9: 14 :**

**Ques. 50 -**** In a mixture of petrol and kerosene, petrol is only 99 litres. If this same quantity of petrol would be presented in another mixture of petrol and Kerosene where total volume would be 198 litres less than the actual mixture then the concentration of petrol in the actual mixture would have been 13.33% point less than that of the new mixture. What is the concentration of petrol in actual mixture ?**

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