Plutus Academy

1. A mixture contains 80% acid and rest water. Part of the mixture that should be removed and replaced

by same amount of water to make the ratio of acid and water 4 : 3 is

80% श 4 : 3

(a) 𝟏

𝟑rd (b) 3

𝟑

𝟕rd (c)

𝟐

𝟑rd (d)

𝟐

𝟕th

2. A and B are two alloys of gold and copper prepared by mixing metals in the ratio 7 : 2 and 7 : 11

respectively. If equal quantities of the alloys are melted to form a third alloy C, the ratio of gold and

copper in C will be

A B श 7 : 2 7 : 11

C C

(a) 5 : 7 (b) 5 : 9 (c) 7 : 5 (d) 9 : 5

3. In a laboratory, two bottles contain mixture of acid and water in the ratio 2 : 5 in the first bottle and 7 :

3 in the second. The ratio in which the contents of these two bottles be mixed such that the new mixture

has acid and water in the ratio 2 : 3 is

श श 2 : 5 7 : 3

2 : 3

(a) 4 : 15 (b) 9 : 8 (c) 21 : 8 (d) 1 : 2

4. The average salary of all the staff in an office of a corporate house is Rs.5,000. The average salary of the

officers is Rs.14,000 and that of the rest is Rs.4,000. If the total number of staff is 500, the number of

officers is.

Rs.5,000 Rs.14,000

श Rs.4,000 500

(a) 10 (b) 15 (c) 25 (d) 50

5. A jar contains 10 red marbles and 30 green ones. How many red marbles must be added to the jar so that

60% of the marbles will be red?

60%

(a) 25 (b) 30 (c) 35 (d) 40

6. Nitin bought some oranges at Rs.40 a dozen and an equal number at Rs.30 a dozen, he sold them at Rs.45

a dozen and made a profit of Rs.480. The number of oranges (in dozen), he bought, was

Rs.40 Rs.30

(a) 48 (b) 60 (c) 72 (d) 84

7. Two vessels contain milk and water in the ratio 3 : 2 and 7 : 3. Find the ratio in which the contents of the

two vessels have to be mixed to get a new mixture in which the ratio of milk and water is 2 : 1.

MIXTURE & ALLIGATION BY MOHIT SHARMA SIR(SSC ,BANK,CDS,RAILWAY, CAT,MAT ETC…)

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MATHS BY MOHIT SHARMA SIR

(a) 2 : 1 (b) 1 : 2 (c) 4 : 1 (d) 1 : 4

8. Out of nine persons, 8 persons spent Rs.30 each for their meals. The ninth one spent Rs.20 more than the

average expenditure of all the nine. The total money spent by all of them was

(a) Rs.260 (b) Rs.290 (c) Rs.292.50 (d) Rs.400.50

9. In a school with 600 students, the average age of the boys is 12 years and that of the girls is 11 years. If

the average age of the school is 11 years and 9 months, then the number of girls in the school is

वर्ष वर्ष वर्ष

(a) 450 (b) 150 (c) 250 (d) 350

10. Sourav purchased 30 kg of rice at the rate of Rs.10 per kg and 35 kg at the rate of Rs.11 per kg. he mixed

the two. At what price per kg (in Rs.) should he sell the mixture to make a 30% profit in the transaction?

30%

(a) 12.5 (b) 13 (c) 13.7 (d) 14.25

11. Prakash lends a part of Rs.20,000 at 8% simple interest and remaining at 𝟒

𝟑% simple interest. His total

income after a year was Rs.800. Find the sum lent at 8%.

श Rs.20,000 श 80% श श 𝟒

𝟑%

Rs.800 8% श(a) Rs.8,000 (b) Rs.12,000 (c) Rs.6,000 (d) Rs.10,000

12. 20 litres of a mixture contains 20% alcohol and the rest water. If 4 litres of water be mixed in it, the

percentage of alcohol in the new mixture will be

20% शश

(a) 33𝟏

𝟑% (b) 16

𝟐

𝟑% (c) 25% (d) 12

𝟏

𝟐%

13. There are two containers of equal capacity. The ratio of milk to water in the first container is 3 : 1, in the

second container 5 : 2. If they are mixed up, the ratio of milk to water in the mixture will be

(a) 28 : 41 (b) 41 : 28 (c) 15 : 41 (d) 41 : 15

14. Three Science classes A, B and C takes a Life Science test. The average score of class A is 83. The average

score of class B is 76. The average score of class C is 85. The average score of class A and B is 79 and

average score of class B and C is 81. Then the average score of classes A, B and C is

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A, B C A 83 B

76 C 85 A B 79 B C 81 A, B

C

(a) 81.5 (b) 81 (c) 80.5 (d) 80

15. 60 kg of an alloy A is mixed with 100 kg of alloy B. If alloy A has lead and tin in the ratio 3 : 2 and alloy

B has tin and copper in the ratio 1 : 4, the amount of tin in the new alloy is

60 A B A

B

(a) 53 kg (b) 44 kg (c) 80 kg (d) 24 kg

16. Three glasses of equal volume contain acid mixed with water. The ratios of acid and water are 2 : 3, 3 : 4

and 4 : 5 respectively. Contents of these glasses are poured in a large vessel. The ratio of acid and water

in the large vessel is

श

(a) 411 : 540 (b) 401 : 544 (c) 417 : 564 (d) 407 : 560

17. Two blends of a commodity costing Rs.35 and Rs.40 per kg. respectively are mixed in the ratio 2 : 3 by

weight. If one fifth of the mixture is sold at Rs.46 per kg and the remaining at the rate of Rs.55 per kg.

the profit percent is

श𝟏

𝟓श

श(a) 50 (b) 30 (c) 40 (d) 20

18. In an examination average marks obtained by the girls of a class is 85 and the average marks obtained

by the boys of the same class is 87. If the girl and boys are in the ratio 4 : 5, average marks of the whole

class (approximately) is closest to

(a) 85 : 9 (b) 86.1 (c) 86.4 (d) 86.5

19. 300 grams of sugar solution has 40% of sugar in it. How much sugar should be added to make ti 50% in

the solution?

300 40% 50%

(a) 40 gram (b) 10 gram (c) 60 gram (d) 80 gram

20. Two bottles contain acid and water in the ratio 2 : 3 and 1 : 2 respectively. These are mixed in the ratio 1

: 3. What is the ratio of acid and water in the new mixture?

श

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(a) 7 : 13 (b) 11 : 57 (c) 23 : 37 (d) 1 : 3

21. In two types of brass, the ratio of Copper to zinc are 8 : 3 and 15 : 7 respectively. If the two types of brass

be melted and mixed in the ratio 5 : 2 a new type of brass is obtained. The ratio of copper to zinc in this

new type of brass is

श

(a) 3 : 2 (b) 2 : 3 (c) 3 : 4 (d) 5 : 2

22. An hour-long test has 60 problems. If a student completes 30 problem in 25 minutes, then the required

seconds he has taken on average for computing each of the remaining problems is

श श श श

(a) 70 seconds/ 70 (b) 50 seconds/50

(c) 40 seconds/40 (d) 30 seconds/30

23. An Army of 12000 consists of Europeans and Indian. The average height of European is 5 feet 10 inches

and that of an Indian is 5 feet 9 inches and that of the whole army is 5 feet 9𝟑

𝟒 inches. Then the number of

Indians in the army is?

12000

9𝟑

𝟒

(a) 3000 (b) 4000 (c) 5500 (d) 2700

24. A sum of Rs.4,000 is lent out in two parts, one at 8% simple interest and the other at 10% simple interest.

If the annual interest is Rs.352. The sum lent at 8% is

Rs.4000 श 8% 10%

Rs.352 श 8%

(a) Rs.2900 (b) Rs.2200 (c) Rs.2400 (d) Rs.3100

25. There are three bottles of mixture of syrup and water of ratio 2 : 3, 3 : 4, 7 : 5. 10 Litres of first and 21

Litres of second bottles are taken. How much quantity from third bottles is to be taken so that final

mixture from three bottles will be of ratios 1 : 1.

2 : 3, 3 : 4, 7 : 5

(a) 25 Litres (b) 20 Litres (c) 35 Litres (d) 30 Litres

26. The average monthly salary of all the employees in a factory is Rs.8840. If the average salary of all the

officers is Rs.15000 and that of the remaining employees is Rs.8000 then what is the percentage of the

officers among the employees?

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शश

(a) 12% (b) 15% (c) 8𝟏

𝟑% (d) 16%

27. Solution A contains 10% acid and solution B contains 30% acid. In what ratio should solution A be mixed

with Solution B to obtain a mixture with 25% acid?

A 10% B 30% A B

25%

(a) 1 : 2 (b) 3 : 1 (c) 1 : 3 (d) 2 : 1

28. In what ratio should coffee powder costing Rs.2500/kg be mixed with coffee powder costing Rs.1500/kg

so that the cost of the mixture is Rs.2250/kg?

(a) 1 : 4 (b) 4 : 1 (c) 3 : 1 (d) 1 : 3

29. In a class of 50 students there are 22 girls who scored an average of 35 marks in the test. What is the

average marks of the boys if the class average is 42 marks?

50

(a) 50 (b) 52.5 (c) 47.5 (d) 55

30. A beaker contains acid and water in the ratio 1 : x. when 300 ml of the mixture and 50 ml of water are

mixed, the ratio of acid and water becomes 2 : 5 What is the value of x?

1 : x 300 ml 50 ml

x

(a) 2 (b) 1 (c) 3 (d) 4

31. A mixture is composed of 11 parts of pure milk and 2 parts of water. If 35 litres of water were added to

the mixture then the new mixture will contain twice as much pure milk as water, then how many litres of

pure milk does the original mixture contain?

शश श

(a) 110 (b) 55 (c) 220 (d) 70

32. If a dairy mixes cow’s milk which contains 10% fat with buffalo’s milk which contains 20% fat, then the

resulting mixture has fat (120/7)% of fat. What ratio was the cow’s milk mixed with buffalo’s milk?

श 10% 20%

(120/7)%

(a) 2 : 5 (b) 1 : 5 (c) 2 : 3 (d) 2 : 1

33. In what ratio should tea costing Rs.300/kg be mixed with tea costing Rs.200/kg so that the cost of the

mixture is Rs.225/kg?

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300

(a) 3 : 1 (b) 1 : 3 (c) 1 : 4 (d) 2 : 1

34. A drum contains 80 litres of ethanol. 20 litres of this liquid is removed and replaced with water. 20 litres

of this mixture is again removed and replaced with water. How much water (in litres) is present in this

drum now?

(a) 45 (b) 40 (c) 35 (d) 44

35. An alloy is made by mixing metal A costing Rs2000/kg and metal B costing Rs400/kg in the ratio A : B

= 3 : 1. What is the cost (in Rs) of 8 kilograms of this alloy?

B A : B = 3 : 1

(a) 1600 (b) 9800 (c) 6400 (d) 12800

36. A jar contains a blend of a fruit juice and water in the ratio 5 : x. When 1 litre of water is added to 4 litres

of the blend the ratio of fruit juice to water becomes 1 : 1. What is the value of x?

5 : x

x

(a) 3 (b) 1 (c) 2 (d) 4

37. An alloy contains copper and tin in the ratio 3 : 2. If 250 gm of copper is added to this alloy then copper

in it becomes double the quantity of tin in it. What is the amount (in gm) of tin in the alloy?

(a) 250 (b) 750 (c) 1000 (d) 500

38. If X beakers of 100 ml containing 1 : 4 acid-water solution are mixed with y beakers of 200 ml containing

3 : 17 acid-water solution then the ratio of acid to water in the resulting mixture becomes 19:91 Find X:Y.

1: 4 X Y

X : Y

(a) 5 : 3 (b) 3 : 5 (c) 7 : 13 (d) 13 : 7

39. In what ratio should 20% ethanol be mixed with 40% ethanol solution to obtain a 28% ethanol solution?

28% 20% 40%

(a) 2 : 3 (b) 8 : 5 (c) 3 : 2 (d) 5 : 8

40. The average weight of a class of 50 students is 48.6 kg. If the average weight of the 20 boys is 54 kg, then

find the average weight (in kg) of the girls in the class.

50

(a) 40 (b) 46 (c) 45 (d) 42

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41. In what ratio, sugar costing Rs.60 per kg be mixed with sugar costing Rs.42

per kg such that by selling the mixture at Rs.56 per kg there is a gain of 12%?

किस अनुपात में, रु 60 प्रकत किग्रा िीमत वाली चीनी, रु 42 प्रकत किग्रा वाली चीनी िे साथ कमकित किया

जाना चाकिए कजससे कि कमिण िो रु 56 प्रकत किग्रा पर बेचिर 12% िा लाभ िो?

(a) 8 : 9 (b) 5 : 6

(c) 5 : 7 (d) 4 : 5

42. The number of students in a class is 75, out of which 33𝟏

𝟑% are boys and the rest are girls. The

average score in mathematics of the boys is 66𝟐

𝟑% more than that of the girls. If the average score

of all the students is 66, then the average score of the girls is:

एि िक्षा में छात्ो ों िी सोंख्या 75 िै, कजसमें से 33𝟏

𝟑% लड़िे िैं और बािी लड़कियाों िैं। लड़िोों िे गकणत में

औसत अोंि लड़कियो ों िी तुलना में 66𝟐

𝟑% अकिि िै। यकि सभी छात्ो ों िा औसत स्कोर 66 िै, तो लड़कियो ों

िा औसत स्कोर िै:

(a) 58 (b) 55

(c) 52 (d) 54

43. The ratios of copper to zinc in alloys A and B are 3 : 4 and 5 : 9, respectively. A and B are taken in

the ratio 2 : 3 and melted to form a new alloy C. What is the ratio of copper to zinc in C?

कमि िातु A और B में ताोंबे और जस्ता िे अनुपात क्रमशः 3: 4 और 5: 9 िैं। A और B िो 2: 3 िे अनुपात में

कलया जाता िै और एि नए कमििातु C िो बनाने िे कलए कपघलाया जाता िै। C में ताोंबे और जस्ता िा अनुपात

क्या िै?

(a) 27 : 43 (b) 8 : 13

(c) 3 : 5 (d) 9 : 11

44. Alloy A contains copper and zinc in the ratio of 4:3 and alloy B contains copper and zinc in the ratio

of 5:2. A and B are taken in the ratio of 5:6 and melted to form a new alloy. The percentage of zinc in

the new alloy is closest to:

मिश्र धात ुA िें 4: 3 के अनुपात िें ताांबा और जस्ता है और मिश्र धातु B िें 5: 2 के अनुपात िें ताांबाऔर जस्ता है। A और B को 5: 6 के अनुपात िें मिया जाता है और एक नया मिश्र धातु बनाया जाता है।नए मिश्र धातु िें जस्ता का प्रततशत है:

(a) 36.8 (b) 54

(c) 34.2 (d) 35

45. 40 litres of 60% concentration of acid solution is added to 35 litres of 80% concentration of acid

solution. What is the concentration of acid in the new solution?

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60% साांद्रता के अम्ि घोि के 40 िीटर को, 80% साांद्रता के अम्ि घोि के 35 िीटर िें मििाया जाता है। नए घोि िें अम्ि की साांद्रता क्या है?

(a) 69% (b) 66%

(c) 𝟔𝟗𝟏

𝟑% (d) 𝟔𝟔

𝟐

𝟑%

46. How many kg of salt costing Rs28 per kg must be mixed with 6.4 kg of salt costing Rs16 per kg, so

that selling the mixture at Rs29.90, there is a gain of 15%?

15%

(a) 35 (b) 33

(c) 32 (d) 31

47. A vessel contains a 32litre solution of acid and water in which the ratio of acid and water is 5:3. If

12litres of the solution are taken out and 7𝟏

𝟐 litres of water are added to it, then what is the ratio of

acid and water in the resulting solution?

7𝟏

𝟐

(a) 4 : 7 (b) 8 : 11

(c) 4 : 9 (d) 5 : 6

48. Two-third of the number of employees of a company are males and the rest are females. If 𝟑

𝟖 of the

male employees and 𝟐

𝟓 of the female employee are temporary employees and the total number of

permanent employees is 740, the 𝟕

𝟏𝟓 of the total number of the employees exceeds the number of

temporary female employees by:

एक कां पनी के किषचाररयों की सांख्या का दो-ततहाई पुरुर् हैं और बाकी िहहिाएां हैं। यहद पुरुर् किषचाररयों का 𝟑

𝟖 और िहहिा किषचारी का 𝟐

𝟓 अस्थायी किषचारी हैं और स्थायी किषचाररयों की कुि सांख्या

740 है, तो 𝟕

𝟏𝟓किषचाररयों की कुि सांख्या अस्थायी िहहिा किषचाररयों की सांख्या से ककतना अधधक है:

(a) 320 (b) 308 (c) 400 (d) 340

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49. In a school, 𝟒

𝟗 of the number of students are girls and the rest are boys.

𝟑

𝟓 of

the number of boys are below 12 years of age and 𝟓

𝟏𝟐 of the number of girls are 12

years or above 12 yeas of age. If the number of students below 12 years of age is

480, then 𝟓

𝟏𝟖 of the total number of students in the school will be equal to:

एि सू्कल में, छात्ो ों िी सोंख्या में 𝟒

𝟗 लड़कियाों िैं और बािी लड़िे िैं। लड़िोों िी सोंख्या िा

𝟑

𝟓 ,12 वर्ष

से िम िै और लड़कियो ों िी सोंख्या िा 𝟓

𝟏𝟐 , 12 वर्ष या 12 वर्ष से अकिि िै। यकि 12 वर्ष से िम आयु

िे छात्ो ों िी सोंख्या 480 िै, तो सू्कल में िुल छात्ो ों िी सोंख्या िा 𝟓

𝟏𝟖 िे बराबर िोगा:

(a) 240 (b) 315 (c) 225 (d) 270

50. In an office, 𝟓

𝟖of the total number of employees are males and the rest are females.

𝟐

𝟓 of the number

of males and non-technical workers while 𝟐

𝟑 of the number of females are technical workers. What

fraction of the total number of employees are technical workers?

एक कायाषिय िें, किषचाररयों की कुि सांख्या के 𝟓

𝟖 पुरुर् हैं और बाकी िहहिाएां हैं। पुरुर्ों और गैर-

तकनीकी श्रमिकों की सांख्या का 𝟐

𝟓 जबकक िहहिाओां की सांख्या का 𝟐

𝟑 तकनीकी कायषकताष हैं।

किषचाररयों की कुि सांख्या का ककतना हहस्सा तकनीकी किषचारी हैं?(a)

𝟏

𝟐 (b)

𝟑

𝟖

(c) 𝟓

𝟖 (d)

𝟐

𝟓

51. The average age of 120 students in a group is 13.56 years.

35% of the number of students are girls and the rest are boys. If the ratio of the average age of boys and girls is 6:5, then what is the average age (in years) of the girls?

एक सिूह िें 120 छात्रों की औसत आयु 13.56 वर्ष है। छात्रों की सांख्या का 35% िड़ककयाां हैं और बाकी िड़के हैं। यहद िड़के और िड़ककयों की औसत आयु का अनुपात 6: 5 है, तो िड़ककयों की औसत आयु (वर्ों िें) क्या है?

a) 10 b) 12c) 11.6 d) 14.4

𝟑

𝟖

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