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3(x + 6) + 2(x + ) = 64
⇒ 3x + 18 + 2x + 6 =64
⇒ 5x + 24 = 64
⇒ 5x = 64  24
⇒ 5x = 40
Here, 3(2 – 5p) –2 (1 – 6p) = 1
⇒ 6  15p  2 + 12p =1
⇒ 4  3p = 1 ⇒ 3p = 4 1
If 8 is subtracted from three times a number the result is 13. What is number?
Let the number be x.
∴ 3x  8 = 13 ⇒ 3x = 13 + 8
⇒ 3x = 21
The sum of three consecutive natural numbers is 114. Which is the greatest number?
Let the number are x, x + 1, x+ 2.
∴ x + x 1 + x + 2 = 114
⇒ 3x +3 = 114 ⇒ 3x = 114  3
Greatest number = 37 + 2 = 39
The length of a rectangular field is 5m more than its breadth. If the perimeter of the field is 74 m what is its length?
Let the breadth be x m.
Length = (x + 5)
Perimeter of rectangle = 74
⇒ 2(x + 5 + x) = 74
⇒ 2x + 5 = 37 ⇒ 2x = 37  5
⇒ 2x = 32
Length = 16 + 5 = 21m
If 9 is added to twice of a certain number, the result is 57, what is that number?
Let the number be x.
2x + 9 = 57 ⇒ 2x = 57– 9 = 48
x = 24
If 7 is subtracted from a number, we get 37, then what is that number?
Let the number be x.
∴ x  7 = 37 ⇒ x = 37 + 7 = 44
A man is thrice as old as his daughter. 5 years ago the man was four times as old as his daughter, what is the age of the daughter?
Let the age of daughter be x years.
∴ Man's age = 3x.
and 5 years ago, daughter's age = x5
∴ Man's age = 3x —5
⇒ 3x —5= 4x —20 = 4x —3x = — 5 + 20
⇒ x =15 years
Karan’s father is thrice as old as Karan. After 14 years his age will be twice that of his son. What is the age of Karan?
Let the age of karan be x years.
Father’s age = 3x years
After 14 years,
3x +14 = 2(x –14)
⇒ 3x + 14 = 2x + 28
⇒ x = 28  14
⇒ x = 14 years
The sum of three consecutive even numbers is 78. Which number is smallest among them?
Let the three consecutive even numbers are
x, x + 2, x + 4.
∴ x + x + 2 + x + 4 =78
⇒ 3x = 78  6
⇒ 3x = 72
Five times the price of a radio is Rs 170 more than three times its price. What is the price of the radio?
Let the price of the ratio be Rs x.
5x =170 + 3x
⇒ 2x =170
The length of a rectangular park is thrice its breadth. If the perimeter of the park is 168m, what is its breadth?
Let the breadth be x m
Length = 3xm
Perimeter of rectangular park = 168
Kiran multiplies a certain number by 17 and adds 4 to the product, she gets 225. What is that number?
Let the number be x.
∴ x × 17 + 4 = 225
⇒ 17x = 225  4
⇒ 17x = 221
What is the sum of the expressions 3a – 2b + 5c, 2a + 5b – 7c and –a – b + c?
Required result
= 3a –2b + 5c + 2a +5b –7c – a – b + c
= 4a + 2b – c
What is the value of 2a – [3b –{a – (2c – 3b) + 4c – 3 (a – b – 2c)}]
Required result
= 2a–[3b–{a – (2c + 3b) + 4c –3a + 3b + 6c}]
= 2a –[3b–{–2a +6b +8c}]
= 2a –[3b +2a – 6b – 8c]
= 2a –[2a–3b–8c] = 2a –2a + 3b +8c
= 3b + 8c
What is the value of xy – [yz – zx –{yx – (3y – xz) – (xy – zy)}]?
xy – [ yz – zx – {yx – (3y – xz) – (xy – zy)}]
= xy – [ yz – zx – {yx – 3y + xz– xy + zy}]
= xy – [ yz – zx – yx + 3y – xz + xy – zy]
= xy + 2xz –3y
If a number is tripled and the result is increased by 7, we get 70, then what is the number?
Let the number be x.
∴ 3 × x + 7 = 70
⇒ 3x = 70  7
⇒ 3x = 63
A wire of length 86cm is bent in the form of a rectangle such that its length is 7 cm more than its breadth. What is its length ?
Let the breadth be x.
∴ Length = x + 7
Perimeter of wire = 86
∴ Length = x + 7 = 18 + 7 = 25 cm
43 tests

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