0
Q:

What is the compound interest earned at the end of 3 years?

I. Simple interest earned on that amount at the same rate and for the same period is Rs. 4500.

II.The rate of interest is 10 p.c.p.a.

III.Compound interest for 3 years is more than the simple interest for that period by Rs.465.

A) I and II only B) II and III only
C) I and III only D) Either II or III only

Answer:   D) Either II or III only



Explanation:

 

 

 

 

 

 

I. gives, S.I for 3 years = Rs. 4500.

 

 

 

II. gives, Rate = 10% p.a.

 

 

 

III. gives, (C.I.) - (S.I.) = Rs. 465.

 

 

 

Clearly, using I and III we get C.I. = Rs. (465 + 4500).

 

 

 

Thus, II is redundant.

 

 

 

Also, from I and II, we get sum =

 

 

 

100 x 4500

 

 

 

= 15000.

 

 

 

10 x 3

 

 

 

Now C.I. on Rs. 15000 at 10% p.a. for 3 years may be obtained.

 

 

 

Thus, III is redundant.

 

 

 

Either II or III is redundant.

Q:

Two boxes contain 4 and 16 balls respectively. Two balls in the first box and four in the second, are black. If a box is chosen randomly and two balls are drawn at random from it, what is the
probability that at least one ball is black if the ball is not replaced?

A) 11/20 B) 43/120
C) 77/120 D) 9/20
 
Answer & Explanation Answer: C) 77/120

Explanation:

At least one black can be chosen in two ways from each box:
Now, probability of choosing at least one black ball from first box 

= 1/2 × [ (2C1× 2C1)/4C2 + 2C2/ 4C2 ]= 5/12

Probability of choosing at least one black ball from 2nd box
= 1/2 × [(4C1×12C1)/16C2 + 4C2/ 16C2] = 9/40

Final probability

= 5/12 + 9/40 = (50 + 27)/120 = 77/120

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4 3487
Q:

Train A, travelling at 84 kmph, overtook train B, traveling in the same direction, in 10 seconds. If train B had been traveling at twice its speed, then train A would have taken 22.5 seconds to overtake it. Find the length of train B, given that it is half the length of train A.

A) 180 m B) 100 m
C) 200 m D) 150 m
 
Answer & Explanation Answer:

Explanation:

Let speed of train B be x m/s And length of train B be y m
Then length of train A is 2y m
Speed of train A = 84 × 5/18 = 210/9 m/s = 70/3 m/s
A.T.Q, (2y+y)/10 = 70/3 − x .............(i)
and (2y+y)/ 22.5 = 70/3 − 2x ................(ii)
solving (i) and (ii), y = 50 m

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0 3333
Q:

A solid sphere of radius 6 cm is melted and re-casted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 5 cm and its height is 32 cm, find the uniform thickness of the cylinder ?

A) 3 cm B) 1.5 cm
C) 1 cm D) 2.5 cm
 
Answer & Explanation Answer: C) 1 cm

Explanation:

Let, inner radius of cylinder be ‘x’ cm.
4/3 π(6)3 = π × 32 (52 − x2)

or, (4 × 6 × 6 × 6) / (3 × 32) = 25 − x2 or, x2 = 25 − 9
or, x = 4 cm
Hence, thickness = 5 – 4 = 1 cm.

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0 1033
Q:

X and Y entered into partnership with Rs. 700 and Rs. 600 respectively. After another 3 months, X withdrew two- sevenths of his stock but after 3 months, he puts back three-fifths of what he had withdrawn. The total profit at the end of the year is Rs. 726. How much of this should X receive?

A) Rs. 336 B) Rs. 366
C) Rs. 633 D) Rs. 663
 
Answer & Explanation Answer: B) Rs. 366

Explanation:

Profit ratio X & Y = (700 × 3) + (700 × 5/7× 3) + (700× 5/7 + 200 × 3/5 )× 6 : 600 ×12
X:Y= 7320 : 7200= 183:180
∴ X’s share from profit = 183 × 726/(183+180) = Rs. 366.

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1 4474
Q:

Cost price of a pen is 50 Rs. and that of notebook is 140 Rs. If pen is sold at 200% profit, then to purchase 10 such note books how many pens are required to sell if only profit money is used to buy notebooks?

A) 14 B) 18
C) 15 D) 20
 
Answer & Explanation Answer: A) 14

Explanation:

C.P. of 10 note books ⇒ 140 × 10 = 1400 Rs.
Profit on selling one pen ⇒ 50×200/100 = Rs 100
Number of pen required ⇒ 1400/100 = 14

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0 1607
Q:

Length of two trains are 150 m and 200 m respectively and the ratio (shorter: longer) of their speed is 2 : 5. If they cross each other in opposite direction in 15 second then in what time faster train will overtake the slower train.

A) 20 seconds B) 25 seconds
C) 32 seconds D) 35 seconds
 
Answer & Explanation Answer: D) 35 seconds

Explanation:

Let speed of slower train = 2x
⇒ speed of faster train = 5x
ATQ, (150 + 200)/(2x + 5x) = 15
x = 10/3
Time required=350/[50/3–20/3]= 35 seconds

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0 1405
Q:

If length of a rectangle is decreased by 6 cm we get a square and the area of square formed is 252 cm2 less than the area of square formed when breadth of the original rectangle is increased by 6 cm. Find the perimeter of the rectangle.

A) 66 cm B) 88 cm
C) 80 cm D) 72 cm
 
Answer & Explanation Answer:

Explanation:

Let length and breadth of rectangle be L cm
and B cm respectively So, ATQ
Area1= (L-6)×B
But this is square, so L-6=B
Area1= (L-6) × (L-6)
Case 2, Area2= L × (B+6),
L=B+6
So, Area2= L × L,
Given, Area2-Area1= 252(L)2-(L-6)2=252
Solving this, L= 24
B= 18
Perimeter= 2(L+B)= 2(24+18)= 84 cm

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2 2483
Q:

Breadth of a rectangle is equal to the diagonal of the square whose side is 2.5√2 cm. Ratio between length and breadth of rectangle is 3 : 1. Find the area of the rectangle (in cm2).

A) 75 B) 90
C) 85 D) 80
 
Answer & Explanation Answer: A) 75

Explanation:

Diagonal of Square = Side √2= 2.5√2 × √2= 5 cm
Breadth = 5 cm
Length of rectangle = 5 × 3 = 15 cm
Area of rectangle = 15 × 5 = 75 cm2

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