Proportional Reasoning — Practice

Question 1

Simplify 48 : 84 to its lowest form.

Accepted Answer

✦ Answer: HCF(48, 84) = 12. Divide both: 48/12 = 4, 84/12 = 7. Simplified ratio = 4 : 7.

Question 2

What is 30% of 250?

Accepted Answer

✦ Answer: 30% of 250 = (30/100) × 250 = 75.

Question 3

If 8 metres of cloth cost ₹560, find the cost of 12 metres.

Accepted Answer

Step 1 — Unitary method.
  8 metres → ₹560
  1 metre → ₹560 / 8 = ₹70
  12 metres → ₹70 × 12 = ₹840

Step 2 — Verify with proportion.
  8/560 = 12/y → 8y = 6720 → y = ₹840 ✓

✦ Answer: 12 metres cost ₹840.

Question 4

A shopkeeper bought a watch for ₹1,200 and sold it for ₹1,500. Find the profit percentage.

Accepted Answer

Step 1 — Identify values.
  CP = ₹1,200
  SP = ₹1,500

Step 2 — Calculate profit.
  Profit = SP − CP = 1500 − 1200 = ₹300

Step 3 — Calculate profit %.
  Profit % = (Profit / CP) × 100
           = (300 / 1200) × 100
           = 25%

Step 4 — Verify.
  25% of 1200 = 300 ✓
  CP + Profit = 1200 + 300 = 1500 = SP ✓

✦ Answer: Profit percentage = 25%.

Question 5

Rohan deposited ₹25,000 in a bank that offers 6.5% simple interest per annum. (a) Calculate the interest after 4 years. (b) Find the total amount in his account. (c) After how many years will the amount become ₹35,400?

Accepted Answer

Part (a) — Calculate SI for 4 years.
  SI = (P × R × T) / 100
     = (25000 × 6.5 × 4) / 100
     = 6,50,000 / 100
     = ₹6,500

Part (b) — Amount after 4 years.
  A = P + SI = 25000 + 6500 = ₹31,500

Part (c) — Find time T for A = ₹35,400.
  SI needed = 35400 − 25000 = ₹10,400
  Apply SI formula: 10400 = (25000 × 6.5 × T) / 100
  10400 = 1625T
  T = 10400 / 1625 = 6.4 years

Step — Verify Part (c).
  SI in 6.4 years = (25000 × 6.5 × 6.4)/100 = 10,400 ✓
  Amount = 25000 + 10400 = 35,400 ✓

✦ Answer: (a) SI = ₹6,500. (b) Amount after 4 years = ₹31,500. (c) Amount becomes ₹35,400 after 6.4 years.

Practice — Proportional Reasoning

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