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 two-fifth of its present?

Correct Answer: 26

Explanation:

Let the number of hens be x and the number of cows be y

Then, x + y = 48 .... (i)

  and 2x + 4y = 140   ⟹   x + 2y = 70 .... (ii)

Solving (i) and (ii) we get: x = 26, y = 22.

∴ The required answer = 26.

Correct Answer: 175

Explanation:

Suppose the man works overtime for x hours.

Now, working hours in 4 weeks = (5 x 8 x 4) = 160.

∴ 160 x 2.40 + x x 3.20 = 432

⟹ 3.20x = 432 - 384 = 48

⟹ x = 15.

Hence, total hours of work = (160 + 15) = 175.

Correct Answer: 512

Explanation:

Let total number of children be x

Then, x x	1	x =	x	x 16   ⟺  x = 64.
	8		2

∴ Number of notebooks =	1	x2 =	❨	1	x 64 x 64	❩	= 512.
	8			8

Correct Answer: ¹⁄₇

Explanation:

Original share of 1 person =	1
	8

New share of 1 person =	1
	7

Increase =	❨	1	-	1	❩	=	1
		7		8			56

∴ Required fraction =	(1/56)	=	❨	1	x	8	❩	=	1
	(1/8)			56		1			7

Correct Answer: Rs. 3900

Explanation:

Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.

Then, 10x = 4y   or   y =	5	x.
	2

∴ 15x + 2y = 4000

⟹ 15x + 2 x	5	x = 4000
	2

⟹ 20x = 4000

∴ x = 200.

So, y =	❨	5	x 200	❩	= 500.
		2

Hence, the cost of 12 chairs and 3 tables = 12x + 3y

    = Rs. (2400 + 1500)

    = Rs. 3900.

Correct Answer: Rs. 2400

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.

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

Correct Answer: Rs. 240

Explanation:

Let C's share = Rs. x

Then, B's share = Rs.	x	,   A's share = Rs.	❨	2	x	x	❩	= Rs.	x
	4			3		4			6

∴	x	+	x	+ x = 1360
	6		4

⟹	17x	= 1360
	12

⟹ x =	1360 x 12	= Rs. 960
	17

Hence, B's share = Rs.	❨	960	❩	= Rs. 240.
		4

Correct Answer: 4

Explanation:

3 ^{x - y} = 27 = 3 ³    ⟺    x - y = 3 ....(i)

3^{x + y} = 243 = 3⁵    ⟺    x + y = 5 ....(ii)

On solving (i) and (ii), we get x = 4.

Correct Answer: 13

Explanation:

Let (25) ^7.5 x (5) ^2.5 ÷ (125) ^1.5 = 5 ^x

Then,	(52)7.5 x (5)2.5	= 5x
	(53)1.5

⟹	5(2 x 7.5) x 52.5	= 5x
	5(3 x 1.5)

⟹	515 x 52.5	= 5x
	54.5

⟹ 5^x = 5^{(15 + 2.5 - 4.5)}

⟹ 5^x = 5¹³

∴ x = 13.

Correct Answer: 1

Explanation:

Given Exp.	= x(b - c)(b + c - a) . x(c - a)(c + a - b) . x(a - b)(a + b - c)
	= x(b - c)(b + c) - a(b - c)   .  x(c - a)(c + a) - b(c - a)    .  x(a - b)(a + b) - c(a - b)
	= x(b2 - c2 + c2 - a2 + a2 - b2)   .   x-a(b - c) - b(c - a) - c(a - b)
	= (x0 x x0)
	= (1 x 1) = 1.