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