Grade-10 Compulsory Maths
7th July 2022
Register work
1. Write the formula for finding rate of discount when discounted amount and marked price
are given.
2.
The marked price of an article is Rs x. If a discount of Rs y is allowed on it, what is
the discount percent? Write it.
3. Write the formula for finding rate of discount when selling price and marked price are
given.
4. If marked price (MP), selling price (SP) and discount (d) then write the relation among
MP, SP and d.
5.
If £ 15 = $ 20 and $ 5 = Rs 390, how much pounds can be exchanged for Rs 31200?
6.
If $ 5 = £ 4 and Rs 225 = $ 3, how much pounds (£) will be equal to Rs 5625?
7.
If £ 52 = $ 91 and Rs 2112 = £ 16, how much dollars ($) will be equal to Rs 5280?
8.
If $ 120 = £ 96 and Rs 135 = £ 1, how many dollars will be equal to Rs 486000?
9. The marked price of a Scooter is Rs 2,50000. If the shopkeeper allows 15% discount and
levies 13% value added tax, how much should a customer have to pay to buy the
Scooter? Find it.
10.
After allowing 10% discount on the marked price of a machine and then levying 10%
VAT, the final price of machine becomes Rs 99,000. Find the marked price of the
machine.
11.
If a watch was sold for Rs 1656 after allowing 10% discount on the marked price and
adding 15% VAT, find the discount amount.
12.
A invested Rs 25000 for 3 years at the rate of 12% simple interest per annum and B
invested the same amount for the same time at the rate of 10% annual compound
interest the calculate,
i) Interest received by A
ii) Interest received by B
iii) Without altering time and rate of interest, how much more or less money
should A have to invest for equal interest?
13.
A sum of Rs 50000 amounts to Rs 75000 at a certain rate of simple interest in 5 years.
Find the sum of money that amounts to Rs 96800 at the same rate of compound interest
in 2 years.
14.
The semi-annual compound amount of a sum of money in 1 year is Rs 8820 and in 2
years is Rs 9724.05.
Find the principal and the rate of interest.
15. A person took a loan of Rs 46875. If the rate of the compound interest is 4 paisa per
rupee per year, in how many years will the compound interest be Rs 5853?
16.
If the semi-annual compound interest of Rs 15625 for 1 year and 6 months is Rs 1951,
find the rate of interest.
17. Simplify
7 2x  1  21  7 2x -1
7 2x  10
18. Simplify: (1  x mn ) 1  (1  x n m ) 1
19. Simplify: a) 3 9x -2 y 2  3 3x 5 y  1
𝑥 2𝑎
3
b)
𝑥 2𝑏
3
108m 10 n11  4m 7 n 5
𝑥 2𝑐
20. If a+b+c= d show that 𝑥 2𝑎+𝑥 𝑏−𝑑 +𝑥 𝑑−𝑐 + 𝑥 2𝑏+𝑥 𝑑−𝑐+𝑥 𝑑−𝑎 + 𝑥 2𝑐+𝑥 𝑑−𝑎+𝑥 𝑑−𝑏 = 1
7th July 2022
Grade-10 Compulsory Maths
Register work
1. If ax+1 = a1+y then write the relation of x and y.
2. If xx+a = kx+a then write the relation of x and k.
3. If ma+b = na+b then write the relation of m and n.
4. If (a m  a n )  a p  a x then express x in terms of m, n and p.
5. If (a m  a n )  a p  a x then express x in terms of m, n and p.
6. If (a m  a n )  a p  a x then express x in terms of m , n and p.
7. Simplify:
a b
8. Solve: 7 x 
xa
2
xb
2
343
7x
 b c
1 
b  2 
a 

10.
2
2
xc
2
 ca
xc
2
xa
2
 56
1 
 2
a  2 
b 

9. Prove that: 
xb
x
y

1

a  
b

yx
1

b  
a

xy
a
 
b
xy
a) What is the relation between area of parallelogram and triangle standing on same
base and between same parallels? Write it.
b) What is the relation between the areas of parallelograms standing on same base and
between same parallels? Write it.
c) What is the relation between area of triangles and standing on same base and
between same parallels? Write it.
d) What is the relation between area of rhombus and triangle standing on same base
and between same parallels? Write it.
12.
a) In the given figure,
b) In the given figure, if
the area of ∆PST is
the
13.
area of parallelogram
40cm2, find the length of
PQRS is 32 cm2. Find the
PQ where
area of  SPQ and  PQT.
PQRS is a square.
c) In the given
d) In the given figure,
figure, if RU =
area of ∆LKK = 24cm2
12cm and TA =
and IN = 8cm, find the
4cm, find the area of the rectangle PQRS.
length of IL.
Prove that the parallelograms on the same base and between the same parallels are
equal in area.
14.
Prove that the area of a triangle is one half of the area of a parallelogram standing on
the same base and between the same parallels.
15.
Prove that the triangles on the same base and between the same parallels are equal in
area.
Long Questions:
16.
a)In the figure,
b) In the given figure, AE//BC, AB//DC
AB //CD, prove
and
that the area of
then prove that;
BF//CE,
parallelogram
ABED and area of parallelogram ABCF i) ΔABF  ΔDCE
are equal to each other.
ii) //gram ABCD = //gram FBCE.