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There is a circular pond and a footpath runs along its boundary. A man walks around it exactly once, keeping close to the edge. His each step is 55 cm long and he takes exactly 440 steps to around once then. The diameter of the pond is
Circumference of the outer edge = 55 x440 = 24200 cm
We know that c = 2πr
∴ 24200 = 2 x 22/7 x r
⇒ r = 24200 x 7/2 x 22 = 3850 cm
radius of the outer edge or pond = 3850 cm = 3850/100 = 38.5 m
diameter = 38.5 x 2 = 77 m
Tanya's grandfather was 8 times older to her 16 years ago. He would be 3 times of her age 8 years from now. Eight years ago, what was the ratio of Tanya's age to that of her grandfather?
Let, Tanya age 16 years ago = x
Grandfather's age 16 years ago = 8x
8 years from now, 3(x + 16 + 8) = (8x + 16 + 8)
⇒ x = 48/5
8 years ago ratio was:
⇒ z + 8/8z + 8
⇒ 88/424 = 11/53
Four of the following five are alike in a certain way and hence from a group. Which one does not belong to the group ?
A boat goes 6 km an hour in still water, but it takes thrice as much time in going the same distance against the current. The speed of the current (in km/hr) is
Let the speed of current be x
and the speed of boat = 6 kmph
⇒ Time = D/S
⇒ 3D/6 = D/6  x
⇒ 18  3x = 6
⇒ x = 4 kmph
Hence, speed of current is 4 kmph
What sum of money will become Rs 1352 in 2 yrs at 4% per annum Compound Interest?
CI = Rs 1352
T = 2 years
R = 4% per annum
CI = P[1 + R/100 ]^{T}
1352 = P[ 104/100 ]^{2} = P[ 10816/10000 ]
⇒ P = 1352 x 10000 /10816
⇒ P = Rs 1250
∠BOC = 7x^{o} + 20^{o} ; ∠COA = 3x^{o} and AB is a straight line. Find (∠BOC  ∠COA) .
∠BOC = 7x^{o} + 20^{o}
∠COA = 3x^{o}
we know that
∠BOC + ∠COA = 180^{o} (Linear pair)
7x^{o} + 20^{o} + 3x^{o} = 180^{o}
⇒ 10x^{o} + 20^{o} = 180^{o}
⇒ 10x^{o} = 180^{o}  20^{o} = 160^{o}
⇒ x^{o} = 160^{o} /10^{o} = 16^{o}
∠BOC = (7 x 16) + 20 = 112 + 20 = 132^{o}
∠COA = 3 x 16 = 48^{o}
∠BOC  ∠COA = 132^{o}  48^{o} = 84^{o}
If the letters in the word DOLPHIN are rearranged as they appear in English alphabetical order, which of the following letters, will be the fifth from left?
3 × 4 = 12
12 × 5 = 60
3 × 5 = 15 = x
If Δ denotes =, + denotes > ,  denotes >, □ denotes ≠, × denotes > and ÷ denotes < then a + b c denotes :
A cistern has two taps (which fill it in 12 mins and 15 mins respectively) and an exhaust tap. When all the three taps are opened together, it takes 20 min to fill an emty cistern. How long will the exhaust tap take to empty it?
Let Tap A can fill the cistern in 12 mins.
Let Tap B can fill the cistern in 15 mins.
Let Tap C can empty the cistern in x mins.
∴ 1/12 + 1/15  1/x = 1/20
⇒ x = 10
The difference between the simple interest on a certain sum of money at 6% per annum for 10 years and at 5% per annum for 2 years is Rs. 100. Find the sum
( P x 6 x 10 /100 )  ( P x 5 x 2/100 ) = 100
⇒ 60P  10P = 10000
⇒ 50P = 10000
⇒ P = 200
⇒ Principle = Rs 200
14^{2} + 289 ÷ 17
= 14^{2} + 17^{2} /17
= 196 + 17 = 213
A mother and a doughter working together can complete a work in 4 days. But if the mother works alone, she can complete the work in 6 days. Both of them worked for one day and then the mother had to leave. How long will the daughter take to complete the remaining work?
(M + D)'s one day's work = 1/4
Remaining work = 3/4
M's one day's work = 1/6
D's one day's work = 1/4  1/6 = 1/12
∴ 1/12 th of the work is done by the daughter in 1 day
3/4 th of the work will be done by daughter in
12 x 3/4 = 9 days
In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer.
I. x^{2} + 5x + 6 = 0
II. y^{2} + 3y + 2 = 0
I. x^{2} + 5x + 6 = 0
⇒ x^{2} + 3x + 2x + 6 = 0
⇒ x(x + 3) + 2(x + 3) = 0
⇒ x = 2, 3
Also,
II. y^{2} + 3y + 2 = 0
⇒ y^{2} + 2y + y + 2 = 0
⇒ y(y + 2) + 1(y + 2) = 0
⇒ y = 1, 2
Hence, x ≤ y
Each of the following questions consists of two sets of figures. Figures 1,2,3 and 4 constitute the Problem Set while figures A,B,C,D and E constitute the Answer Set. There is a definite relationship between figures 1 and 2. Establish a similar relationship between figures 3 and 4 by selecting a suitable figure from the Answer Set .
In the following problem, out of the five figures marked 1, 2, 3, 4 and 5, four are similar in a certain manner. However, one figure is not like the other four. Choose the figure which is different from the rest.
In the following questions, select a figure from amongst the four alternatives, which when placed in the blank space of fig. (X) would complete the pattern.
Eight friends A, B, C, D, E, F, G and H are sitting around a circle facing the centre. H is to the immediate left of E who is third to the right of B. C is second to the right of D and is not a neighbour of B. F is second to the right of G and is not a neighbour of C.
Q. Who is second to the right of E?
Find the number in the series which is wrong.
6, 12, 36, 144, 722, 4320, 30240
6, 12, 36, 144, 722, 4320, 30240
The pattern should be
6, 6 × 2 = 12, 12 × 3 = 36, 36 × 4 = 144,
144 × 5 = 720, 720 × 6 = 4320, 4320 × 7 = 30240
Hence, the wrong entry is 722
Find out from amongst the four alternatives as to how the pattern would appear when the transparent sheet is folded at the dotted line.
In the following questions, the symbols $, @, ©, % and # are used with the following meaning as illustrated below:
'P @ Q' means 'P is not smaller than Q'.
'P # Q' means 'P is not greater than Q'.
'P % Q' means 'P is neither greater than nor smaller than Q'.
'P © Q' means 'P is neither smaller than nor equal to Q'.
'P $ Q' means 'P is neither greater than nor equal to Q'.
Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true?
Give answer (1) if only Conclusions I is true.
Give answer (2) if only Conclusion II is true.
Give answer (3) if either Conclusion I or II is true.
Give answer (4) if neither Conclusion I nor II is true.
Give answer (5) if both conclusions I and II are true.
Q.
Statements : V $ W, W @ T, T # H
Conclusions : I. V © T
II. H % W
Read the following table carefully and answer the questions given below.
Q. What was the grand average marks of the five subjects in 1996 ?
Average marks of the five subjects in 1996
Read the following table carefully and answer the questions given below.
Q. The difference in the average marks in History between 1944 and 1995 was exactly equal to the difference in the highest marks in Hindi between which of the following pairs of years ?
Difference in avg marks in History between 1994 and 1995 was 58  49 = 9
Difference in highest marks in Hindi between pair of years = 84  75 = 9
i.e. 1995 and 1992
Read the following table carefully and answer the questions given below.
Q. What was the approximate percentage increase in average marks in History from 1992 and 1993 ?
Difference of Averge marks in History from 1992 and 1993 is = 55  46 = 9.
Approximate percentage increase = 9/46 × 100 = 19.56 ≅ 20
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