Q.
6. (a) For his morning walk Aslam went 110 meters towards
east from his house and then turned right to keep walking for 40 meters before
turning right again. After continuing to walk for 50 more meters, he turned
right again and kept walking for another 120 meters before he sat down on a
bench at the park. How far was the bench located from his house?
Distance
= 100m
(b)
The income of a company decreased by 10% and 15% in two successive years. What
is the percentage of decrease in income after two years? (5)
Successive Percentage
Change Formula: X + Y + XY / 100
Note: Negative
sign (-) for decrease and positive sign (+) for increase.
Decrease
in 1st year = X = -10
Decrease
in 2nd year = Y = -15
Let’s put values in formula:
= X + Y + XY / 100
= - 10 + (-15) + (-10 x -15)/100
= - 10 - 15 + (150)/100
= - 25 + 15/10
= - 25 + 1.5
=
- 23.5
Odd Numbers:
A number which could not divide by 2. For example, 1, 3, 5, 7….
Let’s
divide 273 by 3 = 273/3 = 91
Consecutive odd numbers:
91 + 93 + 95 = 279
87 + 89 + 91 = 267
89
+ 91 + 93 = 273
(b) Find
the missing number in the given series.
12 x 4, 22 x 4, 32
x 4, 42 x 4, 52 x 4, 62 x 4
1x4, 4x4, 9x4, 16x4, 25x4, 36x4
4,
16, 36,
64, 100, 144
(ii)
30, 29, 27, ?, 20, 15
-1 -2 -3 -4 -5
30, 29, 27, 24, 20, 15
+6 +8 +10 +12 +14
1, 7, 15, 25, 37, 51
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(iv) 0, 2, 6, 12, 20, 30, ?
+2 +4 +6 +8 +10 +12
0, 2, 6, 12, 20, 30, 42
------------------------------------------------------------------------------------------------
(v)
48, 24, 72, 36, 108, ?
x 1/2 x 3 x
1/2 x 3 x
1/2
24, 72, 36, 108, 54,
-----------------------------------------------------------------------------------------------
(i)
THRSI : SHIRT
(ii)
GNDREA : DANGER
(iii)
SCHAMOT : STOMACH
(iv)
ONLNDO : LONDON
(v)
HIODALY : HOLIDAY
(d) Sara’s mother is 6 times older than Sara, where as her brother Ali is twice as old as Sara. In three years’ time the sum of their ages will be 72. How old are Sara, Ali and their mother now? (5)(20)
Let
the age of Sara = x,
Age
of Sara’s mother = 6x,
Age of Sara’s brother = 2x,
According
to the given condition: (x+3) + (2x+3) + (6x+3) = 72
9
+ 9x = 72,
9x
= 72 - 9,
9x
= 63
x =
63/9 = 7
Now,
Age
of Sara = x = 7,
Age
of Sara’s mother = 6x = 6(7) = 42,
Age
of Sara’s brother = 2x = 2(7) = 14,
Q.
8. (b) Aslam is willing to use the stylish ceramics tiles in
the lounge of his under-construction house. The shape of the tile is a right
triangle, having the lengths of two legs of 12 cm and 4 cm. Each tile costs Rs.
15. How much will it cost to fill the lounge of 8 meters length and 6 meters
width with these tiles? (5)
Solution:
Size
of Lounge = 8m x 6m = 48m = 4800cm
As
we know, 1m = 100cm
size
of 1 tile = 4cm x 12cm / 2 = 48cm/2 = 24cm
Number
of tiles in 4800cm area = 4800cm/24cm = 200 tiles
Cost
of 1 tile = Rs. 15
Cost
of 200 tiles = 15 x 200 = 3000/- Rs.
(c)
During a sale a clerk was putting new price tags on each item. On one sweater,
he accidentally raised the price by 20%, instead of lowering the price by 20%.
As a result the price on the tag was Rs. 80 too high. What was the original
price of the sweater? (5)
Let
the price of sweater = Z
20%
of Z = 80/- Rs.
20%/20
of Z = 80/20/- Rs.
1%
of Z = 4/- Rs.
1%
x 100 of Z = 100x4 = Rs. 400/-
Hence, original price of sweater = 400/- Rs.
(d) If in a certain language, BROTHER is written as QDGSNQA, then in the same language, SISTER would be written as —–?
A
B C D E F G H I J K L M N O P Q R S T U V W X Y Z
S I S T E R
R H R S D Q
