Equations quiz 1

Sol : Option B
Let the number be x. Then \frac{(x – 5)}{7} = 10

⇒ x = 75. When 5 is subtracted from 75, we get 70.
Also when 70 is divided by 8, the remainder is 6.

Explanations

Let the numbers be x and y, then x + 6y = 47 and 6x + y = 37

on solving two equations

⇒ x = 5 and y = 7

Explanations

Let Manish’s Present age be x years.

Then his age at the time of marriage = (x – 12) years.

Therefore

x =1.5(x - 12)

⇒ x = 36.

Manish’s brother’s age at the time of his marriage = (x – 12) – 8 = (x - 20) = 16 years.

Therefore Manish’s brother’s present age = (16 + 12) years = 28 years.

Explanations

X – W = W – Y

⇒ 2W = X + Y.

Also, X + Y = 60 ⇒ 2W = 60.

So W = 30. But since the value of X cannot be calculated, so we cannot find the difference between the ages of X and W.

Explanations 12 months wages = Rs. 15000 + cycle; and 9 months wages = Rs. 11000 + cycle ⇒ 3 months wages = Rs. 4000, so 12 month wages = Rs. 16000. Therefore price of the cycle = 16000 – 15000 = Rs. 1000.

Explanations Let the four numbers be A, B, C and D. Let A + 5 = B – 5 = 5C = D/5 = x. Then, A = x – 5, B = x + 5, C = x/5 and D = 5x. A + B + C + D = 144 ⇒ (x – 5) + (x + 5) + x/5 + 5x = 144 ⇒ x = 20. Thus, the numbers are 15, 25, 4 and 100. Therefore required difference = (100 – 4) = 96.

Explanations

Explanation Let the length and breadth of the rectangle be x and y cm, respectively. Then, (x – 8) (y + 6) = xy or 6x – 8y = 48 ........................... (i) Also, (x – 8) = (y + 6) [Sides of Square] or x – y = 14........... (ii) From (i) and (ii), x = 32 and y = 18. Perimeter of the original rectangle = 2(x + y) = 100 cm

Explanations Let the number of fruit baskets be x, the number of cookies baskets bowls be y and the number of chips baskets be z. Now, x + y + z = 122 ....... (i) 3x = 4y = 7z ..................................... (ii) From (i) and (ii), we have x = 56, y = 42, z = 24. Thus, total number of guests = 3x = 4y = 7z = 168.

Explanations According to question, we have A - 20 = B + 20 ⇒ A – B = 40............................... (i) And 3(B – 40) = (A + 40) ⇒ 3B – 120 = A + 40 or A – 3B = - 160........................... (ii) From (i) and (ii), we get A = 140 and B = 100