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Solutions

Overview

Step-by-step NCERT solutions for Finding the Unknown (Chapter 15, NCERT Class 7 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the Finding the Unknown textbook chapter.

Solved

What these solutions cover

All 41 questions in Finding the Unknown are solved in the PDF. Here's what's inside, exercise by exercise:

Unknown Weights — Balance Scales

  1. A sack is placed on one side of a balance scale together with a 2 kg weight. The other side holds a 10 kg weight and a 2 kg weight, and the scale is balanced. Find the weight of the sack. (Fig. 7.9)
  2. Three sacks of equal weight are on one side of a balance scale. The other side has two sacks (same weight) and a 10 kg weight and a 4 kg weight. The scale is balanced. Find the weight of one sack. [Hint: Remove one sack from each side.] (Fig. 7.10)
  3. Four sacks are on the left side of a balance scale. The right side has one sack, a 1 kg weight, a 10 kg weight, and another 10 kg weight. The scale is balanced. Find the weight of one sack. [Hint: Remove objects so that sacks are only on one plate.] (Fig. 7.11)
  4. A balance scale has 90 sacks and a 50 kg weight on the left, and 60 sacks and a 500 kg weight on the right. All sacks have the same weight. Find the weight of one sack. (Fig. 7.12)

Solving Equations — Figure it Out

  1. Solve the equation 3x - 10 = 35 and check the solution.
  2. Solve the equation 5s = 3s and check the solution.
  3. Solve the equation 3u - 7 = 2u + 3 and check the solution.
  4. Solve the equation 4(m + 6) - 8 = 2m - 4 and check the solution.
  5. Solve the equation u/15 = 6 and check the solution.
  6. Find the value of each unknown:
    • (a) 2y = 60
    • (b) -8 = 5x - 3
    • (c) -53w = -15
    • (d) 13 - z = 8
    • (e) k + 8 = 12 - k
    • (f) 7m = m - 3
    • (g) 3n = 10 + n
  7. I am a 3-digit number. My hundred's digit is 3 less than my ten's digit. My ten's digit is 3 less than my unit's digit. The sum of all three digits is 15. Who am I?
  8. The weight of a brick is 1 kg more than half its weight. What is the weight of the brick?
  9. One quarter of a number increased by 9 gives the same number. What is the number?
  10. Given 4k + 1 = 13, find the values of:
    • (a) 8k + 2
    • (b) 4k
    • (c) k
    • (d) 4k - 1
    • (e) -k - 2

Mind the Mistake, Mend the Mistake

  1. Find and correct the mistake in the following solution: 4x + 6 = 10 4x = 10 + 6 4x = 16 x = 4
  2. Find and correct the mistake in the following solution: 7 - 8z = 5 8z = 7 - 5 8z = 2 z = 4
  3. Find and correct the mistake in the following solution: 2v - 4 = 6 v - 4 = 6 - 2 v - 4 = 4 v = 8
  4. Find and correct the mistake in the following solution: 5z + 2 = 3z - 4 5z + 3z = -4 + 2 8z = -2 z = -2/8
  5. Find and correct the mistake in the following solution: 15w - 4w = 26 15w = 26 + 4w 15w = 30 w = 2
  6. Find and correct the mistake in the following solution: 3x + 1 = -12 x + 1 = -12/3 x + 1 = -4 x = -5
  7. Find and correct the mistake in the following solution: 4(4q + 2) = 50 4(4q) = 50 - 2 16q = 48 q = 3
  8. Find and correct the mistake in the following solution: -2(3 - 4x) = 14 -6v - 8x = 14 -8x = 14 + 6 -8x = 20 x = -20/8
  9. Find and correct the mistake in the following solution: 3(7y + 4) = 9 + 5y 7y + 4 = 9/3 + 5y 7y + 4 = 3 + 5y 7y - 5y + 4 = 3 2y = 1/2

Applications and Problem Solving — Figure it Out

  1. Fill in the blanks with integers.
    • (a) 5 x ___ - 8 = 37
    • (b) 37 - (33 - ___) = 35
    • (c) -3 x (-11 + ___) = 45
  2. Ranju is a daily wage labourer. She earns Rs 750 a day. Her employer pays her in 50 and 100 rupee notes. If Ranju gets an equal number of 50 and 100 rupee notes, how many notes of each does she have?
  3. In the given picture, each black blob hides an equal number of blue dots. There are 3 blobs and 4 visible blue dots. If there are 25 dots in total, how many dots are covered by one blob? Write an equation to describe this problem.
  4. Machine
    • (a) takes an input, adds 3, multiplies by 4, then subtracts 5. The example shows input 12 gives output 55. Find the inputs when the outputs are:
    • (i) 43
    • (ii) 75
  5. Machine (b) takes an input, splits into two paths: the top path multiplies by 3; the bottom path adds 3. The two results are then subtracted (top minus bottom). The example shows input 12 gives output 21. Find the inputs when the outputs are: (i) 63 (ii) 227
  6. What are the inputs to these machines?
    • (i) Machine: input -> add 3 -> add 3 -> output = 5
    • (ii) Machine: input -> subtract 4 -> subtract 4 -> output = -11
  7. A taxi driver charges a fixed fee of Rs 800 per day plus Rs 20 for each kilometre travelled. If the total cost for a taxi ride is Rs 2200, determine the number of kilometres travelled.
  8. The sum of two numbers is 76. One number is three times the other number. What are the numbers?
  9. The figure shows a window grill with a total inner height of 34 cm. The top and bottom frame borders are each 3 cm. There are 4 horizontal rods each of thickness 2 cm, with equal gaps between and around them. What is the gap between two rods?
  10. In a restaurant, a fruit juice costs Rs 15 less than a chocolate milkshake. If 4 fruit juices and 7 chocolate milkshakes cost Rs 600, find the cost of the fruit juice and milkshake.
  11. Given 28p - 36 = 98, find the value of 14p - 19 and 28p - 38.
  12. The steps to solve three equations are shown below. Identify and correct any mistakes.
    • (a) 6x + 9 = 66: x + 9 = 11, x = 2
    • (b) 14y + 24 = 36: 7y + 12 = 18, 7y = 6, y = 6/7
    • (c) 4x - 5 = 9x + 8: 4x = 9x + 8 - 5, 4x = 9x + 3, -5x = 3, x = -5/3
  13. Find the measures of the angles of these triangles. Triangle 1: angles are y, y, and (y + 15). Triangle 2: angles are x, (x - 10), and (x + 10).
  14. The Bakhshali Manuscript (300 CE) mentions the following problem. The amount given to the first person is not known. The second person is given twice as much as the first. The third person is given thrice as much as the second; and the fourth person four times as much as the third. The total amount distributed is 132. What is the amount given to the first person?
  15. The height of a giraffe is two and a half metres more than half its height. How tall is the giraffe?
  16. Pattern 1 — Arrow shapes: Position 1 has 5 sticks, each new position adds 4 sticks; sticks(n) = 4n + 1, squares(n) = n.
    • (a) How many squares at position 11?
    • (b) How many sticks at position 11?
    • (c) Can exactly 85 sticks make a position? If yes, which?
    • (d) Can exactly 150 sticks make a position? If yes, which? Pattern 2 — Staircase: Position n has n(n+1)/2 squares and n² + 3n sticks.
    • (a) How many…
  17. A number increased by 36 is equal to ten times itself. What is the number?
  18. Solve these equations:
    • (a) 5(r + 2) = 10
    • (b) -3(u + 2) = 2(u - 1)
    • (c) 2(7 - 2n) = -6
    • (d) 2(x - 4) = -16
    • (e) 6(x - 1) = 2(x - 1) - 4
    • (f) 3 - 7s = 7 - 3s
    • (g) 2x + 1 = 6 - (2x - 3)
    • (h) 10 - 5x = 3(x - 4) - 2(x - 7)
Sample

Worked examples

3 questions from Finding the Unknown, solved step by step.

Solving Equations — Figure it Out

Solve the equation 3x - 10 = 35 and check the solution.

3x - 10 = 35

Add 10 to both sides: 3x = 35 + 10 = 45

Divide both sides by 3: x = 45 / 3 = 15

Check: LHS = 3(15) - 10 = 45 - 10 = 35 = RHS ✓

Answer: x = 15

Mind the Mistake, Mend the Mistake

Find and correct the mistake in the following solution: 4x + 6 = 10 4x = 10 + 6 4x = 16 x = 4

Mistake: The term +6 was added to the RHS instead of subtracted.

When moving +6 from the LHS, its additive inverse (-6) must appear on the RHS.

Correct solution:

4x + 6 = 10

4x = 10 - 6 = 4

x = 4 / 4 = 1

Check: 4(1) + 6 = 10 ✓

Answer: Mistake in the sign when moving 6. Correct answer: x = 1.

Applications and Problem Solving — Figure it Out

Ranju is a daily wage labourer. She earns Rs 750 a day. Her employer pays her in 50 and 100 rupee notes. If Ranju gets an equal number of 50 and 100 rupee notes, how many notes of each does she have?

Let the number of 50-rupee notes = n (and also the number of 100-rupee notes = n).

Total value: 50n + 100n = 750

150n = 750

n = 750 / 150 = 5

Check: 5 x 50 + 5 x 100 = 250 + 500 = 750 ✓

Answer: Ranju has 5 notes of Rs 50 and 5 notes of Rs 100.

All 41 questions in Finding the Unknown are solved step by step in the Solutions PDF above.

Keep solving

More solutions in Ganita Prakash

01Large Numbers Around Us02Arithmetic Expressions03A Peek Beyond the Point04Expressions using Letter Numbers05Parallel and Intersecting Lines06Number Play07A Tale of Three Intersecting Lines08Working with Fractions09Geometric Twins10Operations with Integers11Finding Common Ground12Another Peek Beyond the Point13Connecting the Dots14Constructions and Tilings
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More NCERT Solutions for Class 7

Read the Finding the Unknown textbook chapter / PDF, or browse all NCERT Class 7 Mathematics solutions.

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