CBSE Class 7 Mathematics Finding the Unknown MCQs Set 11

Answer: (c) an equation

Explanation:
1. An equation says that two algebraic expressions are equal, for example 3x + 4 = 7.
2. An expression such as 3x + 4 alone has no equal sign, so it is not an equation.
3. A term and a factor are only parts of an expression.

Teacher's Note:
1. The equal sign is what turns expressions into an equation.
2. Look for '=' to spot an equation quickly.

Answer: (b) 6

Explanation:
1. Left pan = x + x + 5 = 2x + 5 and right pan = 17, so 2x + 5 = 17.
2. Take 5 off both pans: 2x = 12.
3. Two equal boxes weigh 12 units, so one box weighs x = 6.

Teacher's Note:
1. A balanced scale means left total = right total.
2. Check: 6 + 6 + 5 = 17.

Answer: (d) 2n + 1

Explanation:
1. The LHS is the whole expression written to the left of the equal sign.
2. Here that is 2n + 1; the number 99 is the RHS.

Teacher's Note:
1. Take the complete expression, not just one term of it.
2. LHS = left of '=', RHS = right of '='.

Answer: (a) x = 17

Explanation:
1. Subtract 23 from both sides: x = 40 − 23 = 17.
2. Check: 17 + 23 = 40, so the LHS equals the RHS.

Teacher's Note:
1. Undo addition by subtraction.
2. 63 comes from wrongly adding 23 instead of subtracting it.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. R is true: an equation says that the LHS and the RHS have the same value.
2. Adding the same number to two equal values gives two equal results, so A is true.
3. A follows from R, so R is the correct explanation of A.

Teacher's Note:
1. This is the balance idea written in symbols.
2. Equal + same number = still equal.

Answer: (c) 13 matchsticks

Explanation:
1. Put n = 6 in 2n + 1.
2. 2 × 6 + 1 = 12 + 1 = 13 matchsticks.

Teacher's Note:
1. Substitute the position number for n.
2. 12 forgets the '+ 1'.

Answer: (b) Only Statement I is true.

Explanation:
1. Statement I is exactly what solving an equation means, so it is true.
2. Statement II is false: x + 4 = 7 is an equation with a letter-number on one side only.
3. So only Statement I is true.

Teacher's Note:
1. One counter-example is enough to show a statement is false.
2. Unknowns may be on one side or on both sides.

Answer: (d) 8

Explanation:
1. Divide both sides by 7: m = 56 ÷ 7 = 8.
2. Check: 7 × 8 = 56.

Teacher's Note:
1. Undo multiplication by division.
2. 49 and 63 come from subtracting or adding 7.

Answer: (a) (i)-(q), (ii)-(r), (iii)-(p), (iv)-(s)

Explanation:
1. (i) x = 9 − 4 = 5, which is (q).
2. (ii) y = 20 ÷ 5 = 4, which is (r).
3. (iii) z = 1 + 2 = 3, which is (p).
4. (iv) u = 6 × 2 = 12, which is (s). So the answer is (i)-(q), (ii)-(r), (iii)-(p), (iv)-(s).

Teacher's Note:
1. Solve each equation first, then match.
2. Use the inverse operation each time.

Answer: (d) Al-Khwarizmi

Explanation:
1. Around 825 CE, Al-Khwarizmi wrote Hisab al-jabr wal-muqabala.
2. The word al-jabr in this title became our word 'algebra'.

Teacher's Note:
1. Al-jabr means 'restoring'.
2. Brahmagupta and Aryabhata were earlier Indian mathematicians.

Answer: (c) A is true, but R is false.

Explanation:
1. Taking away equal weights from two equal totals leaves equal totals, so A is true.
2. A balanced scale carries the same total weight on both pans, so R is false.
3. So A is true but R is false.

Teacher's Note:
1. Balanced means equal totals on both pans.
2. Test each statement on its own first.

Answer: (b) keeps the equality between the two sides

Explanation:
1. The LHS and RHS already have the same value.
2. Doing the same thing to both of them keeps them equal, so it keeps the equality between the two sides.
3. The solution does not change; this is how we solve equations.

Teacher's Note:
1. Think of adding the same weight to both pans.
2. Division must be by a non-zero number.

Answer: (c) x = 9

Explanation:
1. Add 9 to both sides: 4x = 36.
2. Divide both sides by 4: x = 9.
3. Check: 4 × 9 − 9 = 36 − 9 = 27.

Teacher's Note:
1. Undo the subtraction first, then the multiplication.
2. 4.5 comes from subtracting 9 instead of adding it.

Answer: (d) 6 units

Explanation:
1. Left pan = 3s + 4 and right pan = s + 16, so 3s + 4 = s + 16.
2. Remove one sack from each pan: 2s + 4 = 16.
3. Remove 4 units from each pan: 2s = 12, so s = 6 units.

Teacher's Note:
1. Remove equal sacks first, then equal weights.
2. Check: 18 + 4 = 22 and 6 + 16 = 22.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. Multiplying both sides by 15 gives u = 6 × 15 = 90, so A is true.
2. R is also a true fact.
3. But A uses multiplication to undo division, not addition and subtraction, so R does not explain A.

Teacher's Note:
1. A true reason may still be the wrong reason.
2. Multiplication and division are the inverse pair used here.

Answer: (c) Only Statement I is true.

Explanation:
1. y + 1 = 6 gives y = 5, and 3y = 15 gives y = 5, so Statement I is true.
2. Doing the same operation on both sides keeps the solution the same, so Statement II is false.
3. So only Statement I is true.

Teacher's Note:
1. Solve both equations to compare.
2. Equivalent equations share the same solution.

Answer: (b) when an added term is removed from one side, its additive inverse appears on the other side

Explanation:
1. Subtracting 7 from both sides removes +7 from the LHS.
2. On the RHS it appears as −7, the additive inverse of 7.
3. So the step is correct because an added term removed from one side appears on the other side as its additive inverse.

Teacher's Note:
1. 'Moving a term across' is really subtracting it from both sides.
2. The sign changes when it crosses.

Answer: (b) (i)-(r), (ii)-(s), (iii)-(p), (iv)-(q)

Explanation:
1. (i) x + 9 = 15: subtract 9 from both sides (r).
2. (ii) x − 9 = 15: add 9 to both sides (s).
3. (iii) 9x = 15: divide both sides by 9 (p).
4. (iv) \( \frac{x}{9} \) = 15: multiply both sides by 9 (q). So the answer is (i)-(r), (ii)-(s), (iii)-(p), (iv)-(q).

Teacher's Note:
1. Use the inverse of the operation applied to the unknown.
2. Add ↔ subtract, multiply ↔ divide.

Answer: (a) 18 km

Explanation:
1. Let the distance be k km. Then 12k + 60 = 276.
2. Subtract 60 from both sides: 12k = 216.
3. Divide both sides by 12: k = 18 km. Check: 12 × 18 + 60 = 216 + 60 = 276.

Teacher's Note:
1. Remove the fixed charge first.
2. 23 km comes from forgetting the fixed ₹60.

Answer: (d) A is false, but R is true.

Explanation:
1. A is false: x + 4 = x + 5 has no solution at all, and x + 1 = 1 + x is true for every x.
2. R is true: with s = 0, both 5s and 3s equal 0.
3. So A is false but R is true.

Teacher's Note:
1. Some equations have no solution, some have every number as a solution.
2. Check R by substituting.

Answer: (d) Both statements are true.

Explanation:
1. The 50 is added only once, whatever the number of people, so it is a fixed (delivery) charge. Statement I is true.
2. Taking the number of friends as f (with 5 family members) gives 25(f + 5) = 450, a different equation for the same situation. Statement II is true.
3. So both statements are true.

Teacher's Note:
1. A fixed charge is the constant term.
2. Different unknowns give different equations but the same real answer.

Answer: (a) the term 6 was removed from the LHS without changing its sign

Explanation:
1. Removing +6 from the LHS means subtracting 6 from both sides, so −6 must appear on the RHS.
2. The student wrote +6, so the term 6 was removed from the LHS without changing its sign.
3. Correctly: 4x = 10 − 6 = 4, so x = 1.

Teacher's Note:
1. A term changes its sign when it crosses the equal sign.
2. Always check the answer by substitution.

Answer: (c) x = 4

Explanation:
1. Here A = 7, B = 2, C = 3, D = 18.
2. x = \( \frac{18 - 2}{7 - 3} \) = \( \frac{16}{4} \) = 4.
3. Check: 7 × 4 + 2 = 30 and 3 × 4 + 18 = 30.

Teacher's Note:
1. Match A, B, C, D carefully from the equation.
2. 16 is only the numerator; do not stop there.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Add 100 to both sides: 400 + 6x = 10x. Subtract 6x: 400 = 4x. So R is true.
2. Dividing by 4 gives x = 100, so the price of a horse is ₹100 and A is true.
3. A is obtained directly from R, so R correctly explains A.

Teacher's Note:
1. Collect unknowns on the side with the bigger coefficient.
2. Check: 300 + 600 = 900 = 1000 − 100.

Answer: (a) 4.5 kg

Explanation:
1. Let the weight be w kg. Then w = \( \frac{w}{3} \) + 3.
2. Multiply both sides by 3: 3w = w + 9. Subtract w: 2w = 9.
3. So w = 4.5 kg. Check: one-third of 4.5 is 1.5, and 1.5 + 3 = 4.5.

Teacher's Note:
1. Translate 'more than one-third of' carefully.
2. Clear the fraction by multiplying both sides by 3.

Answer: (d) (i)-(q), (ii)-(p), (iii)-(r), (iv)-(s)

Explanation:
1. (i) x increased by 36 equals ten times x: x + 36 = 10x (q).
2. (ii) The numbers are n and 3n, so n + 3n = 76, that is 4n = 76 (p).
3. (iii) Two blobs of n dots and 7 visible dots: 2n + 7 = 25 (r).
4. (iv) Fixed ₹800 plus ₹20 per km: 20k + 800 = 2200 (s). So (i)-(q), (ii)-(p), (iii)-(r), (iv)-(s).

Teacher's Note:
1. Turn each sentence into symbols step by step.
2. Look for the fixed part and the changing part.

Answer: (c) 12 units

Explanation:
1. Left pan = 3t, right pan = t + 8, so 3t = t + 8.
2. Remove one tin from each pan: 2t = 8, so t = 4 units.
3. One pan carries 3t = 3 × 4 = 12 units (and the other 4 + 8 = 12).

Teacher's Note:
1. The question asks for the pan total, not one tin.
2. 4 units is a trap: it is the weight of one tin.

Answer: (b) Both statements are true.

Explanation:
1. Doubling both sides of 4k + 1 = 13 gives 8k + 2 = 26, so Statement I is true.
2. Subtracting 2 from both sides of 4k + 1 = 13 gives 4k − 1 = 11, so Statement II is true.
3. So both statements are true.

Teacher's Note:
1. Do the same operation to both sides of the given equation.
2. Check with k = 3: 26 and 11 both work.

Answer: (d) A is false, but R is true.

Explanation:
1. Dividing only 6x and leaving 9 changes the LHS, so A is false. The correct step divides every term: x + 1.5 = 11.
2. R states the correct rule, so R is true.
3. (Solving properly: 6x = 57, so x = 9.5.) So A is false but R is true.

Teacher's Note:
1. Divide the whole side, not just one term.
2. It is often easier to remove the 9 first.

Answer: (a) 5x − 3

Explanation:
1. “ya 5” means 5 times the unknown, that is 5x.
2. “ru 3” is the known number 3, and the dot over it makes it −3.
3. So the expression is 5x − 3.

Teacher's Note:
1. ya marks the unknown, ru marks the constant.
2. The dot sits over the number that is negative.