4

Q1. The statement "7 subtracted from 3 times half a number gives 5" can be written in a linear equation as

• 1) 3x - 7 = 5
• 2) 7 + 3x = 5
• 3)
• 4)

Solution

Let the number be x. Then, 

Q2. 3 times a number added to one fifth of that number gives 55. This statement can be written as

• 1)
• 2)
• 3)
• 4)

Solution

Let the number be x.

Q3. The linear equation for the statement "Twice a number subtracted from 29 gives 11" is

• 1) 2x - 29 = 11
• 2) 11 - 2x = 29
• 3) 29 - 2x = 11
• 4) 2x - 11 = 29

Solution

Let the number be xTwice a number subtracted from 29 is 29 - 2xTwice a number subtracted from 29 gives 11 is written in linear form as 29 - 2x = 11

Q4.

Solution

Multiply both sides by 6 ( L.C.M of 3 and 2) 2 (2x -1) = 3 (x + 2) 4x - 2 = 3x + 6 Transpose 3x to L.H.S and -2 to R.H.S 4x -3x = 6 + 2 x = 8

Q5. Solve the equation:

Solution

The L.C.M of 3, 4 and 2 is 12 Multiply both sides by 12 4[2(x - 5)] - 3(x - 2) = 6 × 9 8(x - 5) - 3(x - 2) = 54 8x - 40 - 3x + 6 = 54 5x - 34 = 54 By transposing 34 to R.H.S, we get 5x = 54 + 34 5x = 88 Thus, x =  

Q6. The solution of the equation 3x + 4 = 25 is

• 1) 6
• 2) 9
• 3) 7
• 4) 8

Solution

3x + 4 = 25Transposing 4 to R.H.S, we get3x = 25  -  43x = 21Dividing both sides by 3, we getx = 7

Q7. The solution of equation 3 (x + 1) - 2(x + 1) = 5 is

• 1) x = 3
• 2) x = 0
• 3) x = 4
• 4) x = 5

Solution

Q8. The ages of Rahul and Karan are in the ratio 7:5. Ten years hence, the ratios of their ages will be 9:7. Find their present age?

Solution

Let Rahul's and Karan's age be 7x and 5x respectively. After 10 yrs, their ages are 7x + 10, 5x + 10 respectively. As per the given condition, Ratio after 10 years is 9:7 So, Cross Multiplying, we get 7(7x + 10) = 9(5x + 10) 49x + 70 = 45x + 90 49x - 45x = 90 - 70 4x = 20 x = 5 Therefore, Rahul's age = 7 × 5 = 35 years Karan's age = 5 × 5 = 25 years

Q9. A man travelled  of his journey by rail,  by a taxi,  by bus and remaining 8 km on foot. What is the total distance covered by man?

Solution

Let the total distance covered by man = x km Distance covered by rail + distance covered by taxi + distance covered by bus + distance covered on foot = total distancex + x +x + 8 = x L.C.M. of 5, 4 and 8 is 40. Thus, the equation becomes 24x + 10x + 5x + 320 = 40x 39x + 320 = 40x Transposing 40x to L.H.S. and 320 to R.H.S., we get -x = -320 x = 320Thus, total distance covered by man = 320 Km

Q10. Sumitra has Rs 34 in denominations of 50 paisa and 25 paisa coins. If the number of 25 paisa coins is twice the number of 50 paisa coins, then how many coins of each type does she has in all?

Solution

Let the number of 50 paisa coins = x Then, number of 25 paisa coins = 2x Total money with Sumitra = Rs 34 = 34 × 100 paise = 3400 paiseFrom the given condition, we have: 50x + 25 × 2x = 3400 50x + 50x = 3400 100x = 3400 x = 34 Number of 50 paisa coins = 34 Number of 25 paisa coins = 2 × 34 = 68