Olympiad Test: Linear Equations In One Variable -1 - Class 7 MCQ

Let the total property be Rs x.

Quantity of nickel in 50 kg of alloy
= 60% of 50 kg = 30 kg
Let the required quantity of lead = x kg
Weight of new alloy = (30 + x ) kg

⇒ 120 + 4x = 150 + 3x
⇒ 4x – 3x = 150 – 120 ⇒ 
x = 30 

Let unit’s digit be x.
Ten’s digit = (9 – x)
Number = 10(9 – x) + 1× x = 90 –10x + x
∴ 90 – 9x + 27 = x × 10 + (9 – x)1.
⇒ 117 – 9x = 10 x + 9 –x
⇒ 117 – 9x = 9x + 9

Let the cost price be Rs x.
∴ x + 5% of x = 714

Let the breadth of rectangle = x
Length = 3x
Perimeter of rectangle = 128 
∴ 2(x + 3x) = 128

Let the total journey be x km.
 

Let the unit’s digit be x.
10’s digit = 8–x.
Number = 10(8–x) + 1×x
= 80 – 10x + x = 80 – 9x
and 80 –9x + 18 = 10 × x + (8–x) 1
⇒ 98 –9x = 10x + 8 –x
⇒ 98 –9x = 9x + 8

Number = 80 – 9×5 = 80 – 45 = 35

Let the number be x
∴ x – 21 = 71 – x
⇒ x + x = 71 + 21 
⇒ 2x = 92

Let the smaller angle be x.
∴ Other angle = x + 20°
Now x  + x + 20° = 180°
⇒ 2x = 160° 
⇒ x = 80° 

Let the number be x.
∴ 5x = x +80
⇒ 5x – x = 80
⇒ 4x = 80

Let the three consecutive odd numbers be x, x +2, x + 4.
∴ x + x + 2 + x + 4 = 99
⇒ 3x + 6 = 99
⇒ 3x = 93 
⇒ x  = 31
∴ The numbers are 31,33,35
Hence, difference = 35 – 31 = 4

Let Simran’s age = 5x
Ranjna’s age = 3x
After 6 years, Simran’s age = 5x + 6
Ranjna’s age = 3x + 6

⇒ 25x = 30 = 21x + 42
⇒ 25x –21x = 42 –30
⇒ 4x = 12

∴ Present age of Ranjana = 3x
= 3 × 3 = 9 years 

Let the number be x. 
∴ 3x + 6 = 84
⇒ 3x = 84 –6 
⇒ 3x = 78