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COMPOUND INTEREST
Q1. Mohan sold his watch at 10% loss. If he had sold it for 45
more he would have made 5% profit. Find the seling price of
the watch.
Q1. Find the compound interest on 7500 for 2 years 4 months
at 12% p.a. reckoned amnnually.
Q6. A man sells two tables at the same price on one he makes a
profit of 10% and other. He suffers a loss of 10%. Find his
loss or gainon whole transaction. Ans.: loss % = 1 %
Q7. The defference between the two selling proces of an article
at a discount of 30% and two successive discounts of 20%
and 10% is 72. Find the list price of article.
Ans.: loss % = 1 %
Q8. Articles are marked which gives a p% of 25% after allowing
certain discounts the price reduces to 12.5%. Find the rate
of discount.
Q9. The cost price of an article is 2400. Which is 20% below
the marked price. If it sold it a discount of 16% in the marked
price. Find : (i) the marked price (ii) the selling price
(iii) The profit %.
Ans.: (i) 3000 (ii) 2520 (iii) 5%
Q10. Find the difference between a single discount of 40% and
two successive discounts of 36% and 4% on
2500.
Ans.: 36 %
Q11. A retailer buys a washing machine liste at Rs. 2400 and get
two successive discounts of 15% and 5% he spends
62
on transportation and sells it at a gain of 13%. Find the
selling price of machine.
Ans.: 2260
Q12. A trader allows a discount of 20% of his goods and still
makes at profit of 25%. Find the profit % made, if he sells his
good at (i) Marked price (ii) at 10% discount.
Q13. Find a single discount equivalent to 20%, 15% and 10%.
Q14. A milkman purchases milk at the rate of 12 per litre and
then mixes 25% water to it. Find his profit percent if he sells
the mixture at 15 per litre.
Q15. A man marks his god at a price that would give him 20%
3
of goods at market price and sells the
5
remaining at 20% discount. Find the gain% on whole
transaction.
Ans.: 10.4%
profit the sells
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Q5. If CP of 30 articles equals to SP of 20 articles. Find his gain
or loss %.
Ans.: gain % = 50 %
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Ans.: loss % = 4 %
Q4. Calculate the interest earned and the amount due if a sum
12500 is interesed for 1 year at 12% p.a. interest being
compounded semi anually.
Q5. Find the difference between compound interest and simple
interest on
5000 for 2 years at 8% per annum payable
yearly.
Q6. A man borrows 5000 at 12% compound interest payable
every six months the repays 1800 at the six months the
repays 1800 at the end of every six months. Calculate the
third payment he has to make at the end of 18 months inordr
to clear the entire loan.
Q7. A man saves 5000 every year and deposits it at the end of
the year at 10% p.a. compound interest calculate the total
amount of his savings at the end of the third year.
Q8. At what rate % compound interest does a sum of money
became 2.25 times of itself in 2 years.
Q9. On what sum of money will the difference between S.I. and
C.I. for 2 years at 5% p.a. be equal to 25.
Q10. A certain sum of money at C.I. amount to 7986 in 3 years.
Find the sum and rate percent.
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Q4. Two houses are bought for 65000 each. The first is sold
at a profit % of 8%. If the average price received for each
house is 66300. Find the gain or loss% on second house.
Q3. Calculate the amount and C.I. on Rs. 15000 in 2 years when
the rate of interest for the successive years is 8% and 9%
p.a. respectively.
Q11. The difference between C.I. and S.I. on 8400 for two years
is 21 at the same rate of interst per year. Find the rate of
interest.
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Q3. A sold a table to B at a profit % of 15% later on sold it backs
to A at a p% of 20% there by gaining Rs. 69. How much did
a pay for it originally.
Ans.: 300
Q2. The simple interst on a certain sum of money for 3 years at
10% p.a. is 3600. Find the amount due and the C.I. on this
sum of money at the same rate after 3 years interest is
compounded annually.
Q1. Solve : 3x – 4y = 10
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Q2. A man bought 40 articles at 150 each the sold 25 of them
at a sloss of 10%. At what price must he sell the remaining
articles so as to gain 20% on the whole.
Ans.: 255
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PROFIT AND LOSS
Q3. Solve
Q12. C.I. on a certain sum of money at 5% per annum for 2 years
is 246 calculate the S.I. on same sum for 3 years at 6% p.a.
SIMULTANEOUS LINEAR EQUATION
5x – 3y = 24
7 8
2 12
 2,

 20
x y
x y
Q2. Solve :
30
44
40
55

 10 ,

 13
xy xy
xy xy
Q4. Solve 65x – 33 y  97 , 33 x – 65y  1
Q5. Solve :
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b
g
5
3
61


4 x  2 y 5 3x  2 y
60
b
g b
g
LINEAR EQUATION ( WORD PROBLEMS)
Q1. A’s age is six times. B’s age 15 years hence A will three times
as old as B, Find their ages.
Q2. In a class there are x-seats. If each students occupies one
seats 5 students remain standing and if two students occupy
one seat, 7 seats are empty.
Q3. Divide 32 into two parts if the larger is divide by the samller
the quotient is 2 and the remainder is 5.
Q4. The age of A & B are in the ratio of 7 : 5 tten years hence the
ratio of their ages will be 9 : 7 find their ages.
Q5. A and B together can complete a work in 8 days A can do it
alone in 12 days. If B alone can do it in x days.
Q6. Sweets are distributed to children if each child receives 10
sweets there are 3 left are but there are 4 sweets less for
each to receive 11. Find the no. of sweets.
Q7. A man earns 600 more than his wife one tenth of Man’ss
salary and one sixth of wife’s salary amount to 1500 which
is saved every month. Find their monthly expenditure.
Q8. How much pure alcohol should be added to 600 ml solution
containng 15% alcohol to make it contains 50% acid.
SIMALTENOUS LINEAR EQUATION
Q1. A man buys postage stamps of denominations 25 paise and
50 paise for 10. He buys 28 stamps in all. Find the number
of 25 paise stamps bought by him.
Q3. The sum of the digits of a number of two digit is one-seventh of the number. The number formed by interchanging
the digits is less than the original number by 18. Find the
number.
Q3. If the numerator and denominator of a fraction are increased
3
. If the numerator and
4
denominator are decreased by 2 and 1 respectively, it
by 2 and 1 respectively, if becomes
becomes

. Find the fraction.
2
Q4. At a certain time in a deer park, the number of hoods and
number of legs of deer and human visitors were counted
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1
5
3


2 x  2 y 3(3 x  2 y)
2
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Q6. Solve :
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ab 2 a 2 b

 a 2  b2
x
y
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(b)
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and it was found that there were 41 hoods and 136 legs.
Find the number of deer and human visitors in the park.
b

0
y
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a
x
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(a) ax  by  a  b
bx  ay  a  b
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Q5. Some amount is distributed equally among students if there
are 8 students less, every one will get 10 more. If there are
16 students more every one will get 10 less. What is the
number of students and how much does each get? What is
the total amount distributed.
Q6. A boat goes 30 km upstream and 44 km downstream in 10
hours. In 13 hours it goes 40 km upstream and 55 km
downstream. Determine the speed of the stream and that of
the boat in stikk water.
Q7. A man after reading 80 pages more than one-third of a book
finds that 60 more pages than what he has already read are
left. Find the number of pages in the book.
Q8. Rohan is eight year older than his sister. In three years be
will be twice as his sistter. How old are they now.
Q9. If one side of a rectangle is reduced by 3m it becomes a
square and the area of the rectangle reduces by 75m2. Find
the sum of the areas of the rectangle and square.
Q10. In an examination, the ratio fo passes to failure was 4 : 1 if 30
less had appeared, and 20 less passed, the ratio of passes
to failures would have been 5 : 1. How maney students
appeared for the examination.
INDICES
5n  3  6  5n 1
.
Ans.: 19
9  5n  2 2  5n
Q2. If x 4 y 2 z 3  49392 , find the values of ‘x’, ‘y’ and ‘z’
Q1. Evaluate :
where ‘x’, ‘y’ and ‘z’ are different positive primes.
Ans.: x = 2, y = 3, z = 7
Q3. If
c h  b27g
2
9n  32  3n / 2
3m
Q4. Show that :
3 2
1
1 x
b a
x
1 x
a b
x
c b

1
1 x
b c
 x ac
b g  4  3  31 . Ans.: x = 4
b g F Ib g F Ib g
F
x I
x
x
G J
G J
Prove that : G J
H x K H x K H x K  1.
1

Solve for x : (i) e 4 j
(ii) 3 :3  9:1
32
a
Q7.
1
. Prove that m –n = 1.
27
1
x
Q5. Solve for ‘x’ : 12
Q6.

3

c a
n
4
4
a b
b
b
c
2 x
3
1
2
b c
c a
c
a
x2
x
Ans.:(i) x  4 (ii) x  2 ,  1
2x
Q8. If 4 
‘y’.
e 16 j
3
6 / y

e 8 j . Find the value of ‘x’ and
2
Ans.: x 
3
4,y
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 1.
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Q4. In an isosceles triangle ABC, AB=AC and D is a point on BC
produced. Prove that: AD2 = AC2 + BD.CD.
1 1 1
   0.
p q r
LOGARITHMS
e
j
2
(ii) log 2 x  4  5
Q1. Find x, (i) log 9 27  x
Q2. Express log10 5 108 in terms of log10 2 and log10 3 .
Q3. Without using the log tables, evaluate :
1
2 log10 5  log10 8  log10 4
2
b g
b x  1g  log b x  1g  log
Q4. Find x, if : (i) log10 x  5  1
(ii) log10
10 11  2 log10 3
10
Q5. Find x, if : x  log 48  3 log 2 
1
log 125  log 3
3
Q6. Given log x  m  n and log y  m  n express the value
of log
10 x
y2
in terms of m and n.
Q7. Given 2 log10 x  1  log10 250 , find (i) x (ii) log10 2x .
Q8. Given log10 x  a and log10 y  b .
(i) Write down 10 a1 in terms of x.
(ii) Write down 10 2b in terms of y..
(iii) If log10 P  2a  b ; express P in terms of x and y..
PYTHAGORAS THEOREM
D
Q2. AD is perpendicular to the side BC of an equilateral ABC .
Prove that 4 AD 2  3 AB 2 .
Q3. In a rhombus ABCD, Prove that AC 2  BD 2  4 AB 2 .
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6c
m
B 12cm C
1
cm
6
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A
Ans.: 3
C
A
D
B
AP 2  CP 2  BP 2  DP 2 .
Q7. In given figure, ABC is triangle in which AD is a median and
AEBC .
A
C
D
E
B
Prove that 2 AB 2  2 AC 2  4 AD2  BC 2 .
Q8. In given figure, ADBC . If D divides BC in the
ratio 1 : 3. Prove that 2 AC 2  2 AB 2  BC 2
A
B
D
C
RECTELINEAR FIGURE
Q1. One angle of an eight - sided polygon is 1000 and the other
angles are equal find the measure of each equal angle.
Ans.: 1400
Q2. In a pentagon ABCDE, AB is parallel to ED and angle B =
140 0. Find the angle C and D, if the
 C :  D = 5 : 6.
Q3.
Q4.
Q1. In given figure D  90 0 , AB = 16 cm, BC = 12 cm, CA =
6cm. Find CD.
cm
16
Q5. In triangle ABC, A  90 0 , CA = AB and D is a point on
AB produced. Prove that ; DC 2  BD 2  2 AB. AD .
Q6. If P is any point inside a rectangle ABCD, prove that ;
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Q12. If 5  p  4  q  20 r ; show that :
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2 xz
Q11. If a x  b y  c z and b 2  ac , prove that y 
.
xz
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Q10. If a x  b, b y  c and c z  a , prove that xyz = 1.
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i
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a 1
a 1
2b 2


Q9. Prove that : a 1  b 1
b2  a 2 .
a 1  b 1
d
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Q5.
Q6.
Q7.
Ans.: 1000, 1200
In a polygon there are 5 right angles and the remaining
angles are equal to 1950 each. find the number of sides in
the polygon.
Ans.: 11
ABCDEF is a regular hexagon. Calculate the magnitude of
each angle of BEF .
Ans.: 300, 600, 900
The number of sides of two regular polygons are in the
ratio 4 : 5 and their interior angles are in the ratio
15 : 16, find the number of sides in each polygon.
Ans.: 8 and 10
Two alternate sides of a regular polygon, when produced,
meet at right angle, find (i) The value of each exterior angle
of the polygon. (ii) the number of sides in the poylgon.
Ans.:(i) 450 (ii) 8
Difference between an exterior angle of (n + 2) sided regular polygon and an exterior angle of (n –1) sided regular
polygon is 60. Find the number of sides in each polygon.
Ans.:15 and 12
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sides AB and AD respectively. Prove that area of triangle
Q8. ABCDE is a regular pentagon. Diagonal AD divides  CDE
b
g
b
g
b
= Area APD  Area BPC
g
Q2. In the given figure, M and N are the mid-points of the sides
DC and AB respectively of the parallelogram ABCD.
N
A
D
B
C
M
E
Q3. Use the following diagram to prove that :
(i) Area of quadrilateral APQD = Area of quadrilateral BPQC.
(ii) Area of APQD =
1
 Area of parallelogram ABCD.
2
Q
D
C
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g
Area APB  Area CPD
B
Q4. In the given figure D is mid-point of side AB of ABC and
BDEC is a parallelogram.
A
F
D
B
C
Prove that : Area of ABC and BDEC is a paralleogram
Prove that : Area of ABC = Area of // gm BDEC.
Q5. In the given figure : AD is meadian of ABC and E is any
point on median AD. Prove that Area
g
=
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b
bABEg
Area ACE .
A
E
B
C
D
Q6. D is the mid-point of side AB of the triangle ABC, E is midpoint of CD and F is mid. point of AE. Prove that :
b
g
b
g
8  Area AFD = Area ABC .
Q7. ABCD is a parallelogram P and Q are the mid-points of
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E
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P
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O
A
intersect each other at point O, If area of POB  40cm 2 .
Find : (i) OP : OC (ii) areas of BOC and PBC
(iii) areas of ABC and parallelogram ABCD.
Q9. In the following figure, BD = 3CD and AE = 2DE.
A
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Q1. P is any point inside a parallelogram ABCD. Prove that :
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Ans.:1 : 2
AR EA
b
1
.
8
Q8. In parallelogram ABCD, P is mid-point of AB.CP and BD
APQ =
ADE
into two parts. Find the ratio
.
ADC
E
B
Find :
Area of ABE
.
Area of ABC
C
D
MENSURATION
Q1. Find the area of a triangle ABC right-angled at B in which
AB = 12 cm. AC = 13 cm. Find also the length of perpendicular BD from B on hypotenuse AC.
Ans : 10 cm2, 4
8
cm
13
Q2. The altitude of an equilateral triangle is 5 3 cm. Find its
area and perimeter.
2
Ans : 25 3 cm , 30 cm
Q3. The sides of a right-angled triangle containing the right
angle are 5x cm and (3x – 1) cm. Calculate the length of
the hypotenuse of the triangle if its area is 60 cm2.
Ans : 17 cm
Q4. In DABC, ÐB = 90° and D is mid-point of AC. If AB = 20 cm
and BD = AD = 14.5 cm, find the area and the perimeter of
DABC.
Ans : 210 cm2, 70 cm
Q5. The base of a triangle field is 3 times its height. If the cost of
cultivating the field at the rate of Rs. 25 per 100 m2 is Rs.
60,000, find its base and height.
Ans : 1200 m, 400 m
Q6. Find the area and perimeter of a square plot of land, the
length of whose diagonal is 14 m. Give your answer correct
to 2 places of decimal.
Ans : 90 m2 39.59 m
Q7. Find the area of a trapezium ABCD in which AB||DC, AB =
10 cm, BC = 8 cm, CD = 12 cm and  BCD = 900.
Ans : 88 cm2
2
Q8. A rectangle of area 105 cm has its length equal to x cm.
Write down its breadth in terms of x. Given that its perimeter is 44 cm, write down an equation in x and solve it
to fi nd th e dimen sions of the rectangle.
Ans :
105
cm, x2 – 22x + 105 = 0, 15 cm, 7 cm
x
Q9. A road which is 7m wide surrounds a circular park whose
circumference is 352m. Find the surface area of the road.
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TRIGONOMETRY
5
Q1. If tan  
, find sec , sec   cos ec
12
Ans.:
Q2. If sin  
13 221
,
12 60
1
3
and cos  
. Find the value of
2
2
tan   tan 
.
1  tan  tan 
Ans.: 2 
3
p sin  q cos p 2  q 2
p

Q3. If tan   , show that
.
P sin  q cos p 2  q 2
q
Q4. If tan A  cot A  5 , find the value of tan 2 A  cot 2 A .
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Ans.: 23
b
g
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Ans.: 0
Q6. Using the measurements given in the adjoining
figure,
D
14
C
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13
5
B
A
find the value of (i) cos , (ii) tan  (iii) cosec
Ans.: (i)
12
4
5
, (ii) , (iii)
13
3
4
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Q7. In the adjoining figure, BD = CD.
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10
cm
77
Q16. Water flows through a cylindrical pipe of internal diameter 7
cm at 36 km/hr. Calculate the time it would take to fill a
cylindrical tank, the radius of whose base is 35 cm and
height 1 m.
Ans : 10 seconds
Q17. A field is 30 m long, 18 m broad. A pit 6 m long, 4 m wide and
3 m deep is dug out from the middle of the field and the
earth remained is evenly spread over the remaining area of
the field. Find the rise in level of the remaining part of the
field in centimetres correct to one decimal place.
Ans : 13.9 cm
Ans.: 3
the level of water.
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Q5. If cos  0.6 , find the value of 5 sin   3 tan  .
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Also find the cost of paving the road at Rs. 50 per m2.
Ans.: 2618m2, Rs. 130900
Q10. The sum of diameters of two circles is 35cm and the differences of circumferences is 22 cm. Find the areas of the two
circles.
Ans.: 346.5cm2, 154 cm2
Q11. A wire is bent to form an equilateral triangle of perimeter 32
cm. If the same wire is bent to form a circle, Find the area
enclosed by the wire. Also find the difference in area of
the two figures.
Ans : 1386 cm2, 547.7 cm2
Q12. A classroom is 10m long, 6m broad and 4m high. How many
students can it accommodate if one student needs 1.5m2 of
floor area? How many cubic metres of air will each student
have?
Ans.: 40, 6 m3
3
Q13. The volume of a cuboid is 1440 cm . Its height is 10 cm and
the cross-section is a square. Find the side of the square.
Ans.: 12cm
Q14. A cylinder has a diameter of 20cm. The area of curved surface is 1000 cm2. Find
(i) the height of the cylinder correct to one decimal place.
(ii) the volume of the cylinder correct to one decimal place.
(Take  to be 3.14)
Ans.: 4998.9 cm3
Q15. A cylindrical jar is 20 cm high with internal diameter 7cm. An
iron cube of edge 5cm is immersed in the jar completely in
the water which was originally 12 cm high. Find the rise in
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A
C
Calculate (i)
B
D
tan ADB
tan ACB
(ii)
tan DAB
tan CAB
Ans.: (i) 2 (ii)
b
gb
g
1
2
Q8. Solve the equation : cosec  2 2 cos3  1  0 . If
Ans.:   300 , 200
00    90 0 .
Q9. If A  30 0 , verify that cos4 A  sin 4 A  cos 2 A .
b
g
Q10. If tan A  B 
b
g
3 , tan A  B  1 and B<A. Find the
value of ‘A’ and ‘B’.
Ans.: A  52.50 , B  7.50
Q11. Without using trigonometric tables evaluate
cos 580 sin 220
cos 380 cos ec520


:
.
0
0
0
sin 32
cos 68 tan 18 tan 350 tan 600 tan 72 0 tan 550
Ans.:
6 3
3
Q13. If x  a cos   b sin  and y  a sin   b cos .
Prove that x 2  y 2  a 2  b 2 .
Aliganj
: 0522-4043477
Aashiyana : 0522-4041077
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