**Q1. The sum of the ages of five children born at the intervals of 3 years is 50. Find the age of younger child.**

(a) 4 years

(b) 8 years

(c) 10 years

(d) None of these

**ANS(a);**

Let the age of the youngest child be x years.

Then, x+(x+3)+(x+6)+(x+9)+ (x+12)= 50

⇒5x+30=50

⇒5x=20

⇒x=4

Required age = 4 years

**Q2.Arun lends Rs 20,000 of two of his friends. He gives Rs 12,000 to the first at 8% p.a. simple interest. Arun wants to make a profit of 10% on the whole. The simple interest rate at which he should lend the remaining sum of money to the second friend is**

(a) 8%

(b) 16%

(c) 12%

(d) 13%

**ANS(d);**

S.I. on Rs 12000

=(12000×8×1)/100=Rs 960

Desired gain on Rs 20000

= 20000×10/100=Rs 2000

∴S.I.on Rs.8000=2000-960=Rs 1040

∴Rate=(S.I.×100)/(Principal×Time)=(1040×100)/8000

=13% per annum

**Q3.A borrows Rs 800 at the rate of 12% per annum simple interest and B borrows Rs 910 at the rate of 10% per annum simple interest. In how many years will their amounts of debts be equal ?**

(a) 18

(b) 11

(c) 22

(d) 10 1/6

** ANS(c);**

Then,

⇒x=22

**Q4. A and B invest in the ratio 3 : 5. After 6 months, C joins the business investing an amount equal to B’s. At the end of the year what will be ratio of the year what will be the ratio of their profits?**

(a) 3 : 5 : 2

(b) 3 : 5 : 5

(c) 6 : 10 : 5

(d) 8 : 10 : 5

**ANS(c); **

Ratio of their profits = 3×12∶5×12∶5×6

=36∶60∶30=6∶10∶5

**Q5. A swimming pool is fitted with three pipes. The first two pipes working simultaneously, fill the pool in the same time as the third pipe alone. The second pipe alone fills the pool 5 hours faster than the first pipe and 4 hours slower than the third pipe. In what time will the second and third pipes together fill the pool?**

(a) 3 hours

(b) 3.75 hours

(c) 4 hours

(d) 4.75 hours

**Q6. A men sells 3 articles. First at a profit of 20%, seconds at a loss of 10% and the third at 25% loss. During the whole transaction he bears a loss of Rs 60. Find the C.P. of each article if their S.P. are same.**

(a) 180, 120, 160

(b) 180, 240, 288

(c) 180, 280, 250

(d) 180, 120, 300

**Q7. In a class of 35 students and 6 teachers, each student got toffees that are 20% of the total number of students and each teacher got toffees that are 40% of the total number of students. How many toffees were there?**

(a) 245

(b) 161

(c) 406

(d) 329

**ANS(D); **

35×20% of 35+6×40% of 35

=245+84=329

**Q8.Milk and water are mixed in vessel A in the ratio of 5 : 2 and in vessel B in the ratio of 8 : 5. In what ratio should quantities be taken from the two vessels so as to form a mixture in which milk and water will be in the ratio of 9 : 4 :**

(a) 7 : 2

(b) 5 : 2

(c) 2 : 7

(d) 2 : 5

**Q9. If the ages of P and R are added to twice the age of Q, the total becomes 59. If the ages’ of Q and R are added to thrice the age of P, the total becomes 68. And if the age of P is added to thrice the age of Q and thrice the age of R, the total becomes 108. What is the age of P?**

(a) 15 yrs

(b) 19 yrs

(c) 17 yrs

(d) 12 yrs

**ANS(d);**

Let the present ages of P, Q & R be P years, Q years and R years respectively.

According to Ist condition of question

P + 2Q + R = 59 …(i)

According to 2nd condition of question

3P + Q + R = 68 …(ii)

According to 3rd condition of the question

P + 3Q + 3R = 108 …(iii)

From (ii), we get

Q + R = 68 – 3P …(iv)

From (iii), we get

P + 3(Q+ R) = 108

P = 3 (68 – 3P) = 108 .. using (iv)

P + 204 – 9P = 108

⇒8P=96

∴P=12

P’s Present age=12 yrs

**Q10. Sachin was twice as old as Ajay 10 years back. How old is Ajay today, if Sachin will be 40 years old 10 years hence?**

(a) 20 years

(b) 10 years

(c) 30 years

(d) 15 years

**ANS(a); **

Let 10 years ago, age of Ajay was ‘x’ years

∴ 10 years ago, age of Sachin = 2x years

Present age of Ajay = (x+ 10) years

Present age of Sachin = 2x + 10

10 years hence, Sachin’s age will be (2x + 10) + 10 years

According to question

2x+10+10=40

⇒2x=20

⇒x=10

=x+10=10+10=20 years