**Q1. a : b = 4 : 9 if 4 is added to both of the numbers then the new ratio becomes 21 : 46. What is the difference between a and b?**

(a) 80

**(b) 100**

(c) 125

(d) 130

**Sol.**

**a/b=4x/9x and (a+4)/(b+4)=21/46**

**a=80 and b=180**

**∴b-a=100**

**Q2.. 6 pumps of Kirlosker can fill a tank in 7 days and 2 similar pumps of USHA can fill the same tank in 18 days. What is the ratio of the efficiency of a Kirlosker pump and a USHA pump?**

**(a) 6 : 7**

(b) 7 : 6

(c) 7 : 54

(d) can’t be determined

**Sol.**

**The number of days required by a single Kirlosker pumps to fill the tank=6×7=42 days and the number of days required by a single USHA pump to fill the same tanks=2×18=36 days.**

**Now, since efficiency is inversely proportional to the number of days. Hence,**

**(Efficiency of on K-pump)/(Efficiency of U-pump)=36/42=6/7**

**Q3. 16 person can reap 1/5th field in 6 days. How many person (with same efficiency) are required to reap rest of the field in 8 days?**

(a) 27

(b) 54

**(c) 48**

(d) 64

**Sol.**

**1/5th field can be reaped by 96 man days**

**∴4/5th field can be reaped by 96×4=384 man days**

**Now, since there are only 8 days so required number of men=384/8=48 men**

**Q4. Six men earn as much as seven women, two women earn as much as three boys, four boys earn as much as five girls. If a girl earns Rs.16 a week, what does a man earn per week?**

**(a) Rs.35**

(b) Rs.20

(c) Rs.40

(d) Rs.30

**Sol.**

**6 men = 7 women;**

**2 women = 3 boys;**

**4 boys = 5 girls;**

**Now earning of a girls per week = Rs. 16**

**so Earning of 1 boy = 5/4*16 = 20**

**Earning of 1 women = 3/2*20 = 30**

**Earning of 1 man = 7/6*30 = 35**

**Q5. Find the arithmetic mean of 8 no.between 1 and 10.**

(a) 2.5

**(b) 5.5**

(c) 3.5

(d) 4.5

**Sol.**

**8 arithmetic mean between 1 and 10**

**= 2,3,4,5,6,7,8,9**

**Their mean = (2+3+4+5+6+7+8+9)/8 = 5.5**

**Q6. I am three times as old as my son. Five years later, I shall be two and a half times as old as my son. Then my age and my son’s age are respectively:-**

(a) 42 yrs, 14 yrs

**(b) 45 yrs, 15 yrs**

(c)36 yrs, 12 yrs

(d) 48 yrs, 16 yrs

**Sol.**

**Let the present age of my son = x yrs.**

**Then,the present age of mine = 3x yrs.**

**(3x+5)=5/2(x+5)**

**x = 15 yrs.**

**Father’s age = 45 yrs.**

**Son’s age = 15 yrs.**

**Q7. A money lender finds that due to a fall in the annual rate of interest from 8% to 7(3/4)%, his yearly income diminishes by Rs. 61.50. His capital is**

(a) Rs. 22400

(b) Rs. 23800

**(c) Rs. 24600**

(d) Rs. 26000

**Sol.**

**Decrease in rate of interest = 8% – 7 ¾ %**

**= 8% – 31/4% = ¼ %**

**Now, ATQ,**

**¼% of capital = Rs. 61.50**

**⇒ Total capital (i.e. 100%) = Rs. 61.50 × 4 × 100 = Rs. 24600**

**Q8. The average age of 40 students of a class is 15 years. When 10 new students are admitted, the average age is increased by 0.2 years. The average age of new students is**

(a) 15.2 years

**(b) 16 years**

(c) 16.2 years

(d) 16.4 years

**Sol.**

**Total ages of 40 students = 40 × 15 = 600 years**

**Let the average age of 10 new students = x yr**

**(600 + 10x)/50 = 15.2**

**600 + 10x = 15.2 × 50**

**600 + 10x = 760**

**x = (760 – 600)/10**

**x = 160/10 = 16 yrs.**

**Q9. A man travels a distance of 24 km at 6 km/hr another distance of 24 km at 8 km/hr and a third distance of 24 km at 12 km/hr. His average speed for whole journey (in km/hr) is**

(a) 8(2/3)

**(b) 8**

(c) 2(10/13)

(d) 9

**Sol.**

**T1 = 24/6 = 4 hrs, T2 = 24/8 = 3 hrs,**

**T3= 24/12 = 2 hrs**

**Average speed = (24 + 24 + 24)/(4 + 3 + 2) = 72/9 = 8 km/hr**

**Q10.HCF and LCM of two numbers are 7 and 140 respectively. If the numbers are between 20 and 45, the sum of the numbers,is**

(a) 70

(b) 77

**(c) 63**

(d) 56

**Sol.**

**H.C.F. × L.C.M. = 7 × 140 = 980**

**= 1st no. × 2nd no. (between 20 & 45)**

**= 28 × 35**

**So, sum of the number = 28 + 35 = 63**