**1. A bag contains some Rs. 5 Coins. Rs. 2 coins and Rs. 1 coins with total number of coins being 52, and the total amount being Rs. 125. The number of five rupee and two rupee coins is 37. The numbers of Rs. 5 coins are ………**

**2.The sum of the ages of A and B is four-third the age of C. The age of B is two-thirds the age of C. If the sum of the ages of the three persons is 35 years, find the age of B.**

**3. There are four numbers P, Q, R andS. P is 1/3rd is of the total of Q, R and S. Q is 1/4th of the total of the P, R and S. R is 1/5th of the total of P, Q and S. If the total of the four numbers is 3480, then find the value of S.**

**4. Ajay and Vijay have some marbles with them. Ajay told Vijay “if you give me x marbles, both of us will have equal number of marbles”. Vijay then told Ajay “if you give me twice as many marbles, I will have 30 more marbles than you would”. Find x.**

**5. A man travelled a total distance of 1800 km by plane, train and bus. He travelled one –third of the whole trip by plane and the distance travelled by train is three-fifth of the distance travelled by bus. Find the distance travelled by bus.**

**6. Ajay bought a total of 12 oranges and 18 bananas for Rs. 84. When the cost of each orange doubles, he could buy 6 oranges and 16 bananas for Rs. 80. Find the cost of each banana.**

**7. The cost of one pen and two books together is Rs. 70. The cost of three pens and nine books together is Rs. 300. Find the difference between the cost of a book and a pen.**

**8. The present average age of a couple and their daughter is 35 years. Fifteen year from now, the age of the number will be equal to the sum of present ages of the father and the daughter. Find the present age of the mother.**

**9. The cost of three pens, four erasers and ten sharpeners is Rs. 75. The cost of six pens. Seven erasers and twenty sharpeners is Rs. 146. Find the cost of each eraser.**

**10. Shyam and Ram have some chocolates with each of them, if shyam gives 5 chocolates of Ram, both will have equal number of chocolates. If Ram gives the same number of chocolates to shyam, shyam would have twice as many chocolates as Ram. Find the number of chocolates Ram has.**

**ANSWERS AND SOLUTION:**

**1.(a)**

Let the number of Rs. 5 coins be x, Rs. 2 coins be y and Rs. 1 coins be Z.

x + y + z = 52 ………………….. (1)

5x + 2y + z = 125 …………………… (2)

x + y = 10 …………..(3) (2) ……….(1)

Gives that 4x + y = 73

x + y = 37

3x = 36

x = 36/3=12

Number of Rs. 5 coins = 12

**2.(b) **

Let the age of A, B and C be a, b and c respectively.

a + b = 4/3c, b = 2/3c

a + b + c = 35 = 4/3c + c = 35

7/3c = 35

C = 15, b = 2/3c = 10.

**3.(b) **

P = 3480/4 = 870

Q = 3480/5 = 696

R = 3480/6 = 580

P + Q + R = 870 + 696 + 580 = 2146

S = 3480 – 2146 = 1334

**4.(b) **

Let the number of marbles with Ajay and Vijay initially be A and V. If Vijay gives x marble to Ajay then vijay and Ajay would have V – x and A + x marbles respectively.

V – x = A + x …………………….. (1)

If Ajay gives 2x marble to Vijay then Ajay and Vijay would have A – 2x and V + 2x marbles respectively.

V + 2x –(A-2x) = 30 = V – A + 4x = 30 ……………… (2)

From (1) we have V – A = 2x

Substituting V – A = 2x in equation (2)

6x = 30 = x = 5.

**5.(d) **

Total distance travelled = 1800 km

Distance travelled by plane = 600 km

Let distance travelled by bus = x

Distance travelled by train = 3x/5

x + 3x/5+ 600=1800

8x/5=1200=x=750 km

**6.(b)**

Let the cost of each orange and each banana be a and b respectively.

12a + 18b = 84

If the cost of each orange doubles, it becomes 2a

6(2a) + 16b = 80

12a + 16b = 80

Substracting equation (2) from (1) we get 2b = 4

**7.(b) **

Let the price of book be y and price of pen be x.

x + 2y = 70

3x + 9y =300

By solving the equations we get x = 10 and y = 30

The difference between the cost of book and pen is 30 – 10 = Rs. 20

**8.(d) **

Let the present age of the father, mother and daughter be f, m and d respectively.

(f+m+d)/3=35

f + m + d = 105 …………………….. (1)

m + 15 = f + d

Substituting f + d as m + 15 in (1), we get 2m + 15 = 105

2m = 90 =m = 45 years

**9.(b) **

Let the cost of each pen, eraser and sharpener b p, e and s respectively.

3p + 4e + 10s = 75

6p + 7e + 20x = 146

Multiplying the first of the above equations by 2 and subtracting the second equation from it, we get e = 4

**10.(a) **

Let the number of chocolates with shyam and Ram be S and R respectively. If Shyam gives 5 chocolates to Ram, he would have S – 5 chocolates and Ram would have R + 5 chocolates.

So S – 5 = R + 5

S – R = 10 …………………… (1)

If Ram gives 5 chocolates to Shyam, he would have R – 5 chocolates and Shyam would have S + 5 chocolates.

S + 5 = 2 (R – 5)

2R – S = 15

Adding (1) and (2) we get R = 25.

Number of chocolates with Ram = 25

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