**Q1. The difference between a two-digit number and the number obtained by interchanging the two digits of the number is 36. What is the difference between the two digits of the number?**

(a) 6

(b) 4

(c) 3

(d) Cannot be determined

**S1. Ans.(b)**

**Sol. **Let the two digit number =xy

According to the question,

10x+y-(10y+x)=36

9x-9y=36

x-y=4

Difference between the digit = 4

**Q2. If the digits of a two-digit number are interchanged, the number so obtained is greater than the original number by 27. If the sum of the two digits of the number is 11, what is the original number?**

(a) 47

(b) 38

(c) 74

(d) Cannot be determined

**S2. Ans.(a)**

**Sol**. Let the two-digit number = xy

According to the question,

10y+x-(10x+y)=27

y-x=3 … (1)

y+x=11 … (2)

By solving it

y=7

x=4

Original number = 47

**Q3. The sum of five consecutive even numbers of Set-A is 220. What is the sum of a different set of five consecutive numbers whose second lowest number in 37 less than double of the lowest number of Set-A?**

(a) 223

(b) 225

(c) 235

(d) None of these

**S3. Ans.(d)**

**Sol.** Let the first number is x than five consecutive even numbers are x,x+2,x+4,x+6,x+8

According to question,

x+x+2+x+4+x+6+x+8=220

⇒5x+20=220

⇒5x=220-20

⇒x=200/5=40

Again, suppose different set of five consecutive even number’s second lowest number = y+2 which is 37 less than double of the lowest number of Set A

=40×2-37=43

∴ First lowest number = 43-1=42

and, Sum = 42 + 43 + 44 + 45+ 46

= 220

**Q4. For what value of K, the number 7236K2 is divisible by 8?**

(a) 7

(b) 5

(c) 4

(d) 9

**S4. Ans.(a)**

**Sol.** We know that number is divisible by 8 if the last three digits of given number divisible by 8

So, 6K2 must be divisible by 8

Hence, K will be equal to 7.

**Q5. A number when divided by a certain divisor left remainder 241, when twice the number was divided by the same divisor, the remainder was 112. Find the divisor.**

(a) 370

(b) 365

(c) 380

(d) 456

**S5. Ans.(a)**

**Sol.** when the number double then the remainder will also be two times of given remainder. But in this case remainder is 112

So, Divisor = 2×241-112

= 370

**Q6. Find the least number which must be added to 15463 so that the resulting number is exactly divisible by 107?**

(a) 52

(b) 71

(c) 55

(d) 19

**S6. Ans.(a)**

**Sol.** Divide 15463 by 107, the remainder is 55, therefore, the number to be added = 107 – 55 = 52.

**Q7. In four consecutive prime numbers that are in ascending order, the product of the first three is 385 and that of the last three is 1001. The largest given prime number is:**

(a) 11

(b) 13

(c) 17

(d) 19

**S7. Ans.(b)**

**Sol.** Factor of 1001 = 7×11×13

Factor of 385 = 5×7×11

So, largest prime number = 13

**Q8. L.C.M. and H.C.F. of two numbers x and y are 3 and 105, respectively. If x+y=36, the value of 1/x+1/y is:**

(a) 1

(b) 1/6

(c) 12/315

(d) 4/35

**S8. Ans.(d)**

**Sol.** L.C.M × H.C.F = x×y

x×y=3×105

= 315

Require answer = 1/x+1/y=(x + y)/xy=36/(3 × 105)=4/35

**Q9. The population of a town increases by 12% during first year and decreases by 10% during second year. If the present population is 50400, what is was 2 years ago?**

(a) 40000

(b) 35000

(c) 50000

(d) None of these

**S9. Ans.(c) **

**Sol.**Let the population of town before 2 years = x

**Q10. Mrs Sharma invests 15% of her monthly salary, i.e., Rs. 4,428 in Mutual funds. Late she invests 18% of her monthly salary on Pension Policies; also, she invests another 9% of her salary of Insurance Policies. What is the total monthly amount invested by Mrs Sharma?**

(a) Rs. 1,13,356.80

(b) Rs. 12,398.40

(c) Rs. 56,678.40

(d) Cannot be determined

**S10. Ans.(b)**

**Sol**. 15% of salary = Rs. 4,428

∴ 42% of salary = (4428/15)×42 = Rs. 12,398.4

**Q11. A discount of 14% on the marked price of an article is allowed and then the article is sold for Rs. 387. The marked price of the article is**:

(a) Rs. 450

(b) Rs. 427

(c) Rs. 500

(d) Rs. 440

**S11. Ans.(a)**

**Sol.** Let the mark price = x

x×(1-14/100)=387

x=450

Mark price = 450

**Q12. In a test, minimum passing percentage for girls and boys is 35% and 40% respectively. A boy scored 483 marks and failed by 117 marks. What are the minimum passing marks for girls?**

(a) 425

(b) 520

(c) 500

(d) None of these

**S12. Ans.(d)**

**Sol.** Passing marks for the boy = 483 + 117

= 600

40% of mark = 600

Total mark = 600/40×100

Passing marks for girl = 1500×35/100

= 525

**Q13. In a certain year, the average monthly income of a person is Rs. 3400 and that for the first eight months is Rs. 3160 and for the last five months is Rs. 4120. The income in the eight month of the year is:**

(a) Rs. 5080

(b) Rs. 6080

(c) Rs. 5180

(d) Rs. 3880

**S13. Ans.(a)**

**Sol.** Income in the eight month = income of first 8 month + income of last 5 month – income of the year

=8×3160+5×4120-12×3400

= 5080

**Q14. In a class of 52 students, the number of boys is two less than the number of girls. Average weight of the boys is 42 kg, while the average weight of all the 52 students is 40 kg. Approximately, what is the average weight of the girls?**

(a) 41 kg

(b) 29 kg

(c) 40 kg

(d) 38 kg

**S14. Ans.(d)**

**Sol**. Let, the number of boys = x

And the number of girls = y

Now, y-2=x and x+y=52

y-2+y=52

2y=54

∴y=27

∴x=25

**Q15. The average marks of 40 students in an English exam is 72. Later it is found that three marks 64, 62 and 84 were wrongly entered as 68, 65 and 73. The average after mistakes were rectified is:**

(a) 70

(b) 72

(c) 71.9

(d) 72.1

**S15. Ans.(d)**

**Sol. **Difference in original number and wrongly entered number

=64+62+84-68-65-73

= 4

Rectified average = 72+4/40

= 72.1