Quantitative Aptitude: Mixture and Alligation Questions Set 9

Mixture and Alligation concept Aptitude Question Shortcut Tricks for NICL, IBPS RRB. SBI PO, IBPS PO, RBI Grade B, Dena Bank PO PGDBF, BOI, Bank of Baroda and other competitive exams

1. A shopkeeper purchase two quantities of rice at the rate of Rs. 280/kg and Rs. 260/kg . In 52 kg of the second quantity, how much rice of the first quantity should be mixed so that by selling the resulting mixture at Rs.300/ kg , he gains a profit of 25%.
   A) 20 kg
   B)26kg
   C)33 kg
   D) 30kg
   E) 18kg
   
   View Answer

     Option B
   Solution:
   profit % = 25/100 = ¼
   CP = 4 and profit = 1
   SP = 5
   Now , SP = 300
   5———300
   1———60
   CP = 4 * 60 = R.240/kg
   Rice 1————— Rice 2
   200——————–260
   ————–240
   20———————40
   1:2
   52 kg of the second quantity .
   so Rice 1 : Rice 2 = 1*26 : 2 * 26= 26 : 52
   Hence , 26 kg of Rice 1 is added in the mixture.
   
   
   
2. If the average weight of  the whole class is 50 kg. And the average weight of boys in the class is 30 kg and the average weight of girls in the same class is 22 kg. What could be the possible strength of boys and girls in the class respectively?
   A) 5 : 8
   B) 5 : 3
   C) 7 : 5
   D) 7 : 6
   E) 9 : 5
   
   View Answer

     Option   B
   Solution:
   No. of boys : No. of girls
   22   —————   30
   ———- 25
   5 —————– 3
   3 : 5
   Hence , the possible strength of the boys and girls in the whole class = 5 : 3
   
3. A woman travels 200 km in 5 hours in two parts. In the first part of the journey, she travels  by car at the speed of 50 km/hr . In the second part of the journey , she travels by bus at the speed of 30 km/hr . How much distance did she travel by bus?
   A) 75 km
   B) 55 km
   C)40 km
   D) 95km
   E) 20 km
   
   View Answer

     Option  A
   Solution:
   speed of car —————- speed of bus
   50 ———————————-  30
   ———————200/5
   10 ———————————– 10
   = 1 : 1
   Time taken by both the vehicles = 5/2 = 2.5 hrs.
   Therefore, distance travelled by bus  =30 * 2.5  = 75 km
   
4. Somnath  bought two different kinds of oil, one is soya oil and another is olive oil.There are two mixtures of these two oils . In the first mixture the ratio of the soya and olive oil is in  the ratio of 3 : 4 and in the second mixture the ratio of the  soya and olive oil is 5 : 6 . If he mixes these two mixtures and makes a third mixture of 36 litres in which the ratio of the soya oil and olive oil is 4 : 5.  Find the quantity of the second mixture that is needed to make 36 litres of third type of mixture.
   A) 25 L
   B) 22 L
   C)34 L
   D) 18 L
   E) 27 L
   
   View Answer

     Option   B
   Solution:
   MixI —————– MixII
   (3/7) —————- (5/11)
   ————–(4/9)
   (1/99)——————(1/63)
   Ratio = 7 : 11
   Required quantity of the second mixture to make the third mixture
   = (11/18)*36 = 22 litres
   
5. A vessel which contains 100 litres of salt and sugar solution in the ratio of 22 : 3 . From the vessel 40 litres of mixture is taken out and 4.8 litres of pure salt solution and pure sugar solution , both are added to the mixture . What is the percentage of the quantity of sugar solution in the final mixture less than the quantity of salt solution?
   A) 72(1/4)%
   B) 78(1/2)%
   C) 70(1/5)%
   D) 74(1/3)%
   E) 79(1/6)%
   
   View Answer

     Option  E
   Solution:
   40 L is taken out remaining 60 L
   salt solution = (22/25)*60 = 52.8 L
   sugar solution = (3/25)*60 = 7.2 L
   On adding salt and sugar solution
   salt solution = 52.8 + 4.8 = 57.6 L
   sugar solution = 7.2 + 4.8 = 12 L
   Require % = (57.6 – 12)/57.6 = 79(1/6)%
   
6. The average marks of the students in four sections P, Q ,R and S together is 60% . The average marks of the students of P, Q, R and S separartely are 45% , 50%, 72% and 80% respectively. If the average marks of the students of  P and  Q together is 48% and that of the students of Q and R is 60%. What is the ratio of number of students in sections A and D ?
   A) 7 : 5
   B) 4 : 3
   C) 2 : 1
   D) 3 : 2
   E)  5 : 3
   
   View Answer

     Option  B
   Solution:
   A —————- D
   45—————80
   ——–60
   20———–15
   4 : 3
   Hence , the required ratio = 4 : 3
   
7. A shopkeeper has two types of wheat . The percentage of first type of wheat is 80% and the percentage of second type of wheat is 60%. If he mixes 28kg of first type of wheat to the 32 kg of second type of wheat , then find the percentage of resultant wheat in the  mixture.
   A) 66
   B) 60.15
   C)75.12
   D) 69.33
   E) 58.05
   
   View Answer

     Option D
   Solution:
   Type I ————- Type II
   60———————–80
   ————-x
   32———————-28
   8 : 7
   7 : 8 (reverse ratio)
   Now,(80-60)*7/(7+8) = 20 *(7/15) = 9.33
   Required % = 60+9.33 = 69.33
   
8. From a container of wine , 8 litres of wine is drawn and replace the  same quantity with  water. This is performed three more times, now the ratio of the quantity  of wine to that of water in the container becomes 16 : 65. What is the initial quantity of wine in the container?
   A) 26 L
   B) 28 L
   C) 24 L
   D) 22 L
   E) 20 L
   
   View Answer

     Option  C
   Solution:
   Let x be the initial quantity of the wine .
   After 4 operations the quantity of wine left = [x{1-(8/x)^4}]L
   => [x{1-(8/x)}^4] =  16 / 81
   =>{1 – (8/x)}^4 =  16/81
   => (x -8)/x = 2/3
   => x = 24 L
9. The price of the diesel is Rs. 70 per litre and the price of the petrol is Rs. 40 per litre. If the profit after selling the mixture at Rs. 75 per litre be 25 %. Find the ratio of the diesel and petrol in the mixture.
   A) 5 : 4
   B) 4 : 3
   C) 3 : 2
   D) 2 : 1
   E) 1 : 3
   
   View Answer

     Option   D
   Solution:
   25% = ¼
   CP = 4, SP = 5
   SP — 5 ===== 75
   1 ====== 15
   CP = 4 * 15 = 60
   Diesel ———— Petrol70 ——————- 40
   ————-60
   20 ——————- 10
   ratio =  2 : 1
   
10. There are two factories, one in India and another in US. Mr. Anish purchased these two factories for total 80 crores. Later on, he sold the Indian factory at the rate of  16% profit and the US factory at 32% profit, thereby he gained  20%. What is the selling price of the factory?
    A) 84 cr.
    B) 75 cr.
    C)69.6 cr.
    D) 68.5 cr.
    E) 70 cr.
    
    View Answer

      Option  C
    Solution:
    Indian Factory ————– US factory
    16———————32
    ————-20
    12———————4
    = 3 : 1
    The CP of Indian Factory = (80/4)*3 = 60 crores
    SP = 69.6 crores
    

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