**Q1. A mixture contains milk and water in the ratio of 9 : 2. 44 lit of mixture is taken out and 12 lit of water is added to it, such that ratio of milk to water becomes 3:1. Now another mixture of 64 lit having milk and water in ratio of 3:5 is added to it. Find ratio of milk to water in the final mixture? **

(a) 32 : 17

(b) 34 : 19

(c) 7 : 4

(d) 24 : 11

(e) 33 : 19

**Q2. Ratio of present age of Simmi & Rimmi is 4 : 3 while ratio of age of Simmi 6 years later to present age of Rina is 3 : 1. Ratio of present age of Rimmi to present age of Rina is 2 : 1. Find average of present age of all the three (in years). **

(a) 37

(b) 36

(c) 32

(d) 34

(e) 38

**Q3. A shopkeeper sells an article at Rs. 720 by making a profit of x% and on interchanging selling price with cost price, it would have a loss of y%. Find the selling price if an article was sold at y% profit whose cost price is Rs.720 (given x : y = 9 : 7) **

(a) Rs. 810

(b) Rs. 800

(c) Rs. 1100

(d) Rs. 880

(e) Rs. 660

**Q4. There are two rectangular fields of same area. The length of first rectangular field is a% less than the length of the second field and breadth of the first field is (4a)% greater than the breadth of the second field. Find the value of ‘a’ if a is non-zero number. **

(a) 60

(b) 75

(c) 80

(d) 90

(e) None of these

**Q5. A sum is divided between Aman and Vikash in the ratio of 3 : 5. Aman purchased a motorbike from his money which depreciates 20% per annum while Vikash invested his amount in a scheme which offers compound interest at 20% per annum. By what percentage, the total sum will change after two years? **

(a) 12%

(b) 14%

(c) 16%

(d) 18%

(e) 20%

**Directions (6-10): Neeraj have some toys which are in the form of different structures. These are cylindrical, conical, spherical. Other than solid conical structure, all two are of both types i.e., hollow as well as solid.**

→ Volume of a conical toy is three times of the volume of a solid cylindrical toy while radius of a solid spherical toy is half than that the radius of a conical toy. Outer radius of hollow cylindrical toys is same as radius of solid spherical toy while average of outer radius and inner radius of hollow cylindrical toys is equal to radius of solid cylindrical toy. Height of cylindrical, conical and hollow cylindrical toys is same i.e, 14c.m

→ Number of solid spherical toys is 20% of total number of toys Neeraj have. Number of hollow spherical toys is 150% more than number of conical toys. Ratio between number of solid cylindrical toys to number of conical toys is 3 : 2. Total number of hollow cylindrical toys is 40% of total number of toys Neeraj have and also ‘20’ more than the total number of solid spherical toys Neeraj have.

→ Volume of a hollow spherical toy is 33,957 cm² whose inner radius is half of its outer radius. Volume of a hollow spherical toy is 5.25 time of volume of conical toy.

**Q6. Find the total space taken by all solid spherical toys? (in cm³) **

(a) 97020

(b) 48510

(c) 72765

(d) 14553

(e) 24255

**Q7. Find the number of conical toys Neeraj have? **

(a) 40

(b) 20

(c) 15

(d) 12

(e) 8

**Q8. Find the curved surface area of one hollow cylindrical toy? (in cm²) **

(a) 616

(b) 1232

(c) 924

(d) 462

(e) 1386

**Q9. Find the ratio between outer radius of hollow spherical toy to radius of solid cylindrical toy? **

(a) 4 : 1

(b) 3 : 2

(c) 3 : 1

(d) 4 : 3

(e) 2 : 1

**Q10. Volume of one hollow cylindrical toy is how much more then volume of one cylindrical toy?(in cm³)**

(a) 4312

(b) 3234

(c) 2696

(d) 2156

(e) 1078

**Solutions**