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NCERT Solutions · Maths Ch 15
Finding The Unknown
38 questions · 4 exercises
Closed
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Ex 15.1
Ex 15.2
Ex 15.3
Ex 15.4
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 15.1 · 2 QUESTIONS
Solving Equations
Q1
Solve these equations and check the solutions. (a) 3x − 10 = 35 (b) 5s = 3s (c) 3u − 7 = 2u + 3 (d) 4(m + 6) − 8 = 2m − 4 (e) u/15 = 6
(5 marks)
Q2
Frame an equation that has no solution. [Hint: 4 more than a number, and 5 more than a number can never be equal!]
(2 marks)
2
EXERCISE 15.2 · 6 QUESTIONS
Forming and Solving Equations
Q3
Write 5 equations whose solution is x = −2.
(3 marks)
Q4
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
(5 marks)
Q5
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 the three digits is 15. Who am I?
(3 marks)
Q6
The weight of a brick is 1 kg more than half its weight. What is the weight of the brick?
(3 marks)
Q7
One quarter of a number increased by 9 gives the same number. What is the number?
(3 marks)
Q8
Given 4k + 1 = 13, find the values of: (a) 8k + 2 (b) 4k (c) k (d) 4k − 1 (e) −k − 2
(3 marks)
3
EXERCISE 15.3 · 9 QUESTIONS
Mind the Mistake, Mend the Mistake
Q9
Mind the Mistake, Mend the Mistake — Equation 1: 4x + 6 = 10; 4x = 10 + 6; 4x = 16; x = 4. Decide whether the steps are correct. If there is a mistake, describe it, correct it and solve.
(3 marks)
Q10
Mind the Mistake — Equation 2: 7 − 8z = 5; 8z = 7 − 5; 8z = 2; z = 4. Find and correct the mistake.
(3 marks)
Q11
Mind the Mistake — Equation 3: 2v − 4 = 6; v − 4 = 6 − 2; v − 4 = 4; v = 8. Find and correct the mistake.
(3 marks)
Q12
Mind the Mistake — Equation 4: 5z + 2 = 3z − 4; 5z + 3z = −4 + 2; 8z = −2; z = −2/8. Find and correct the mistake.
(3 marks)
Q13
Mind the Mistake — Equation 5: 15w − 4w = 26; 15w = 26 + 4w; 15w = 30; w = 2. Find and correct the mistake.
(3 marks)
Q14
Mind the Mistake — Equation 6: 3x + 1 = −12; x + 1 = −12/3; x + 1 = −4; x = −5. Find and correct the mistake.
(3 marks)
Q15
Mind the Mistake — Equation 7: 4(4q + 2) = 50; 4(4q) = 50 − 2; 16q = 48; q = 3. Find and correct the mistake.
(3 marks)
Q16
Mind the Mistake — Equation 8: −2(3 − 4x) = 14; −6v − 8x = 14; −8x = 14 + 6; −8x = 20; x = −20/8. Find and correct the mistake.
(3 marks)
Q17
Mind the Mistake — Equation 9: 3(7y + 4) = 9 + 5y; 7y + 4 = 9/3 + 5y; 7y + 4 = 3 + 5y; 7y − 5y + 4 = 3; 2y = 4 − 3; y = 1/2. Find and correct the mistake.
(3 marks)
4
EXERCISE 15.4 · 21 QUESTIONS
End of Chapter
Q18
Fill in the blanks with integers. (a) 5 × ___ − 8 = 37 (b) 37 − (33 − ___) = 35 (c) −3 × (−11 + ___) = 45
(5 marks)
Q19
Ranju is a daily wage labourer. She earns ₹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 marks)
Q20
In the given picture, each black blob hides an equal number of blue dots. If there are 25 dots in total, how many dots are covered by one blob? Write an equation to describe this problem. (The picture shows 3 black blobs and 4 visible blue dots.)
(3 marks)
Q21
Machine (a): the input goes through +3, then ×4, then −5 to give the output (e.g. input 12 → 15 → 60 → 55). Find the inputs when the output is (i) 43 (ii) 75. Machine (b): the input is multiplied by 3 in one branch and has 3 added in the other branch; the result is (×3 branch) − (+3 branch) (e.g. input 12 → 36 and 15 → 21). Find the inputs when the output is (i) 63 (ii) 227.
(5 marks)
Q22
What are the inputs to these machines? (a) ? → ÷3 → ÷3 = +5 (b) ? → −4 → −4 = −11
(3 marks)
Q23
A taxi driver charges a fixed fee of ₹800 per day plus ₹20 for each kilometre travelled. If the total cost for a taxi ride is ₹2200, determine the number of kilometres travelled.
(3 marks)
Q24
The sum of two numbers is 76. One number is three times the other number. What are the numbers?
(3 marks)
Q25
The figure shows the diagram for a window with a grill. What is the gap between two rods in the grill? (Figure: total height 34 cm; top bar 3 cm; each rod 2 cm; the window shows 6 gaps and 5 rods between them.)
(3 marks)
Q26
In a restaurant, a fruit juice costs ₹15 less than a chocolate milkshake. If 4 fruit juices and 7 chocolate milkshakes cost ₹600, find the cost of the fruit juice and milkshake.
(3 marks)
Q27
Given 28p − 36 = 98, find the value of 14p − 19 and 28p − 38.
(3 marks)
Q28
The steps to solve three equations are shown below. Identify and correct any mistakes. (a) 6x + 9 = 66; x + 9 = 11; x = 11 − 9; 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; 4x − 9x = 3; −5x = 3; x = −5/3
(5 marks)
Q29
Find the measures of the angles of these triangles. (Triangle 1: an isosceles triangle with the two sides marked equal; the apex angle is y and the two base angles are both y + 15. Triangle 2: angles x, x − 10 and x + 10.)
(3 marks)
Q30
Write 4 equations whose solution is u = 6.
(3 marks)
Q31
The Bakhśhāli Manuscript (300 CE): The amount given to the first person is not known. The second person is given twice as much as the first. The third is given thrice as much as the second; the fourth four times as much as the third. The total distributed is 132. What is the amount given to the first person?
(3 marks)
Q32
The height of a giraffe is two and a half metres more than half its height. How tall is the giraffe?
(3 marks)
Q33
Two separate figures show the first few positions in a sequence of arrangements made with sticks. Figure 1: a row of squares ending in a triangle (position 1 has 1 square, position 2 has 2 squares, position 3 has 3 squares, each with a triangle at the end). Figure 2: a staircase of squares (position 1 has 4 squares, position 2 has 7, position 3 has 10). For each figure: (a) How many squares are in position 11? (b) How many sticks are needed for position 11? (c) Can an arrangement be made with exactly 85 sticks? Which position? (d) Can an arrangement be made with exactly 150 sticks? Which position?
(5 marks)
Q34
A number increased by 36 is equal to ten times itself. What is the number?
(2 marks)
Q35
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)
(5 marks)
Q36
Solve the equations to find a path from Start to the End. (The maze has 12 equation cells in 3 columns and 4 rows; each arrow shows the solution of the cell it leaves.)
(2 marks)
Q37
There are some children and donkeys on a beach. Together they have 28 heads and 80 feet. How many donkeys are there? How many children are there?
(3 marks)
Q38
A Magic Trick: Think of any number. Multiply it by 2. Add 10. Divide by 2. Subtract the original number. Add 3. I predict that you now have 8. Can you explain why the trick works? [Hint: Denote the first number thought of by x.]
(3 marks)