**Q1. The sum of remainders obtained on dividing 12112 by 11 and 13223 by 13 is**

**(a) 3**

(b) 4

(c) 5

(d) 2

**Sol.**

**On dividing, 12112 by 11, we get 1 as remainder**

**Sum of remainders 1 + 2 = 3**

**Q2. The difference between the place value of 6 and the face value of 4 in 56431 is**

(a) 999

(b) 5600

**(c) 5996**

(d) 2054

**Sol.**

**Place value of 6 in 56431 = 6000**

**Face value of 4 in 56431 = 4**

**∴ Required difference = 6000 – 4 = 5996**

**Q3. The product of the smallest common multiple and the biggest common factor of 30, 36 and 42 is**

(a) 7460

(b) 7660

(c) 7650

**(d) 7560**

**Sol.**

**Smallest common multiple of 30, 36 and 42 = 6**

**Biggest common factor of 30, 36 and 42**

**= 2 × 2 × 3 × 3 × 5 × 7 = 2160**

**∴ Required product = 2160 × 6 = 7560**

**Q4. When it is 8:49 pm, in Delhi, it is 1:19 am, on the next day in Sydney. What time will be in Sydney when it is 11:19 am in Delhi?**

(a) 3:19 am

**(b) 3:49 am**

(c) 6:29 am

(d) 6:49 am

**Sol.**

**When time in Delhi 8 : 49 pm, then it is 1 : 19 am is Sydney.**

**∴ Difference in time between Delhi and Sydney**

**= 8 : 49 pm – 1 : 19 am = 4 h 30 min**

**∴ Time is Sydney will be = 11 : 19 am to 4 : 30 = 3 : 49 pm**

**Q5. On a map, 1/2 cm shows 125 km on the ground. If two cities are actually 2000 km apart on the ground, then the distance between them on the map is**

(a) 6 cm

(b) 8 cm

(c) 10 cm

(d) 4 cm

**Ans. (b)**

**Sol.**

**According to question, 1/2 cm on a map = 125 km on the ground**

**⇒ If two cities are 2000 km apart on the ground,**

**Then the distance them on the map**

**=2000/125×1/2= 8 cm**

**Q6. There are 660 students in a school. Two-thirds of them are boys. Three-fourths of the number of boys are players and one-fourth of the girls are players. Total number of players in the school is**

(a) 370

**(b) 385**

(c) 395

(d) 330

**Sol.**

**Total number of students in the school = 660**

**Number of boys in school =2/3×660=440**

**∴ Number of girls of school = 660 – 440 = 220**

**Number of boys who are players =3/4×440=330**

**Number of girls who are player =1/4×220=55**

**Total number of players in school = 330 + 55 = 385**

**Q7. Renu wants to lay tiles on the floor of her house which is 9 m long and 7 m wide. Among the following sizes of tiles, which one should she buy so that the floor is tiled without cutting any tile?**

(a) 40 cm × 65 cm

(b) 55 cm × 40 cm

**(c) 35 cm × 45 cm**

(d) 35 cm × 35 cm

**Sol.**

**Area of the floor of the house = 9 × 7 = 63 cm2**

**= 630000 cm2**

**Using option (c),**

**Size of tile should she buy so that the floor is tiled without cutting any tile = 35 × 45 = 1575 cm2**

**Number of complete tiles =630000/1575=400**

**∴ Option (c) is correct.**

**Q8. There are four cuboidal boxes with dimensions (in cm) as given below.**

**Length Breadth Height**

(a) 20 25 18

**(b) 23 20 20**

(c) 20 22 21

(d) 24 20 19

**Sol.**

**Find out the volume of all cuboidal boxes**

**(i) Volume of the first cuboidal box = 20 × 25 × 18 = 9000 cm3**

**(ii) Volume of second cuboidal box = 23 × 20 × 20 = 9200 cm3**

**(iii) Volume of third cuboidal box = 20 × 22 × 21 = 9240 cm3**

**(iv) Volume of fourth cuboidal box = 24 × 20 × 19 = 9120 cm3**

**From option (a), (i) + (iii) = 9000 + 9200 = 18200 cm3**

**Which is not required.**

**From option (b), (ii) + (iii) = 9200 + 9240 = 18440 cm2**

**Which is correct.**

**Hence option (b) is correct.**

**Q9. The length of a rectangle is two times that of a square whose perimeter is 80 cm. If breath of the rectangle is 20 cm, then the area (in cm2) of the rectangle exceeds the area of the square by**

(a) 150

(b) 300

**(c) 400**

(d) 100

**Sol.**

**Perimeter of square = 4 × side**

**80 = 4 × side**

**Side of square =80/4= 20 cm**

**∴ Length of rectangle = 2 × side of square = 2 × 20 = 40 cm**

**⇒ Area of rectangle = 20 × 40 = 800 cm2**

**Area of square = 20 × 20 = 400 cm2**

**∴ Area of rectangle exceeds the area of the square by (800 – 400) = 400 cm2**

**Q10. Haroon went to a fruit shop. He bought 1 1/2 dozen bananas at the rate of Rs. 2.50 per banana, 3 1/2 at Rs. 57.60 per kg, 1 1/2 kg of mangoes at Rs. 75.40 per kg and 750 g of grapes at Rs. 120 per kg. If he gave a note of Rs. 500 to the fruit seller, he will get back**

(a) Rs. 24.85

(b) Rs. 14.95

**(c) Rs. 50.30**

(d) Rs. 28.10

**Sol.**

**Money spent on and half dozen bananas = 18 × 25 = Rs. 45**

**Money spent on three and a half kilogram apples =3 1/2×57.60=7/2×57.60 = Rs. 201.6**

**Money spent on one and half kilogram mangoes 1 1/2×75.40 = Rs. 3/2×75.40 Rs. 113.1**

**Money spent on 750 gram of grapes =750/1000×120 = Rs. 90**

**∴ Money he will get back = 500 – (45 + 201.6 + 113.1 + 90)**

**= 500 – 449.7 = Rs. 50.30**