**1. If p – q = 6 and p^2 + q^2 = 116, what is the value of pq?**

**2.The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?**

**3. If a^2+b^2+c^2= 2(a-b-c)-3, then find the value of 2a-3b+4c.**

**4. To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to three-fifth of its present?**

**5.A sum of Rs. 1360 has been divided among A, B and C such that A gets 2/3 of what B gets and B gets 1/4 of what C gets. B’s share is:**

**6.A man has Rs. 312 in the denominations of one-rupee notes, five-rupee notes and twenty-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?**

**7.Simplfy b – [b -(a+b) – {b – (b – a+b)} + 2a]**

**8.Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed?**

**9 .a * b = 2a – 3b + ab, then 3*5 + 5*3 = ?**

**10.One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,80,000 as total savings, how much has he saved in Public Provident Fund?**

**Note**: Solution will be provided within an hour. you can give your answer in comment section.

**ANSWER AND SOLUTION:**

**1(B)Explanation :**

(a-b)^2=a^2-2ab+b^2

so (p – q)^2 = p^2 – 2pq + q^2

(p – q)^2 = (p^2 + q^2)- 2pq

6^2 = 116 – 2pq

36 = 116 – 2pq

2pq = 80

pq = 40

**2(B)Explanation:**

Let the price of a saree and a shirt be Rs. x and Rs. y respectively.

Then, 2x + 4y = 1600 …. (i)

and x + 6y = 1600 …. (ii)

Divide equation (i) by 2, we get the below equation.

=> x + 2y = 800. — (iii)

Now subtract (iii) from (ii)

x + 6y = 1600 (-)

x + 2y = 800

—————-

4y = 800

—————-

Therefore, y = 200.

Now apply value of y in (iii)

=> x + 2 x 200 = 800

=> x + 400 = 800

Therefore x = 400

Solving (i) and (ii) we get x = 400, y = 200.

so Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.

**3(B)Explanation:**

a^2 + b^2+c^2 = 2(a-b-c)-3

a^2 + b^2+c^2-2(a-b-c)+3=0

a^2 + b^2+c^2-2a+2b+2c+1+1+1=0

(a^2+1-2a)+ (b^2+1+2b)+(c^2+1+2c)= 0

(a-1)^2+(b+1)^2+(c+1)^2= 0

so a = 1, b = -1, c = -1

so 2a – 3b + 4c = 2×1 – ((3x(-1)) + 4x(-1)

= 2 +3 – 4

= 5 – 4

= 1

**4(C)Explanation :**

Let x buckets of water be required ,if the capacity of the bucket is reduced to two-fifth

More buckets, less capacity (Indirect proportion)

Hence we can write as

Capacity 1 : 2/5 } :: x : 25

1×25 = 2/5×x

25 = 2x/5

x=25×5/2 = 62.5

i.e., 62.5 buckets are needed

**5(C)Explanation:**

Let C’s share = Rs. x

Then, B’s share = Rs. x/4 , A’s share = Rs.(2/3 x x/4) = Rs. x/6

so, x/6 + x/4 + x = 1360

=>17x/12 = 1360

=> x =1360 x 12/17 = Rs. 960

Hence, B’s share = Rs. (960/4) = Rs. 240.

**6( A)Explanation :**

Let the number of notes of each denomination be x

Then, x + 5x + 20x = 312

=> 26x = 312

=> x = 312/26 = 12

the total number of notes that he has = 3x = 3 × 12 = 36

**7(D)Explanation:**

b-[b-(a+b)-{b-(b-a+b)}+2a]

=b-[b-a-b-{b-(2b-a)}+2a]

=b-[-a-{b-2b+a}+2a]

=b-[-a-{-b+a}+2a]

=b-[-a+b-a+2a]

=b-[-2a+b+2a]

=b-b

=0

**8(D)Explanation :**

Let n be the total number of children.

More children, less notebooks(Indirect proportion)

If the number children = n, number of books each child will get = n/8

If the number children = n/2, number of books each child will get = 16

Hence we can write as

children n : n/2 } :: 16 : n/8

n×n/8 = n/2×16

n/8 = 16/2 = 8

n = 8×8 = 64

Then, total number of notebooks those were distributed = n×n/8 = 64×64/8 = 64×8=512

**9(C)Explanation:**

= 2(3)-3(5)+(3*5) + 2(5)-3(3)+(5*3)

= 6-15+15+10-9+15 = 31-9 = 22

**10(A)Explanation :**

Let savings in National Savings Certificate = x

and savings in Public Provident Fund = (180000 – x)

1/3 x = 1/2(180000-x)

2x = 3(180000-x)

2x = 540000-3x

5x = 540000

x=540000/5 = 108000

Savings in Public Provident Fund = (180000 – 108000) = 72000