CAT 2026 · Slot 3 · Expected paper

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CAT 2026 Slot 3 Quant: Arithmetic Questions with Solutions

6 questions: Q1, Q6, Q9, Q11, Q17, Q19. Solve each one here: tap the answer, press Check, then open the solution.

Question 1Ratios & Proportion

TITA (type the answer) · +3 / 0 · medium

A vendor has 374 fruits in total, made up of apples, mangoes and oranges. Apples and mangoes are present in the ratio 5:2. She sells 150 apples, 52 mangoes and half of the oranges. The numbers of unsold apples and unsold oranges are then in the ratio 3:2. Find the total number of fruits remaining unsold.

Your answer

Answer and solution

Correct answer: 132

Solution

Answer: 132

1. Set apples=5k and mangoes=2k. The original oranges are 374−7k.

2. After selling, apples=5k−150, mangoes=2k−52, oranges=(374−7k)/2.

3. Apply the remaining ratio: (5k−150)/[(374−7k)/2]=3/2. Thus 4(5k−150)=3(374−7k).

4. Solve 20k−600=1122−21k: k=42. Original stock is 210,84,80.

5. Remaining stock is 60,32,40. Total=132. Check 60:40=3:2.

Why this method works:
The original apples: mangoes ratio introduces one shared multiplier, reducing three stock variables to one after using the total. The unsold ratio must be applied only after subtracting the specified sales; it does not describe the original fruit mix.

Independent check and common trap:
With k=42, original quantities 210+84+80=374. Sales are 150+52+40=242, leaving 374−242=132. This independent total check agrees with 60+32+40 and the remaining apple: orange ratio 3:2.

G Strategy shortcut

Spot: Ratio and Proportion.
Apply: Use one multiplier k: apples=5k, mangoes=2k. Combine the total and the UNSOLD ratio; do not apply 3:2 to the original stock.
Check: With k=42, original quantities 210+84+80=374. Sales are 150+52+40=242, leaving 374−242=132. This independent total check agrees with 60+32+40 and the remaining apple: orange ratio 3:2.

G Strategy: Spot: Ratio and Proportion. Apply: Use one multiplier k: apples=5k, mangoes=2k. Combine the total and the UNSOLD ratio; do not apply 3:2 to the original stock. Check: With k=42, original quantities 210+84+80=374. Sales are 150+52+40=242, leaving 374−242=132. This independent total check agrees with 60+32+40 and the remaining apple: orange ratio 3:2.

Question 6Ratios & Proportion

MCQ · +3 / −1 · easy

In one month, the earnings of Ravi, Sunil and Manoj are in the ratio 8:6:5. They contribute 15%, 12% and 18% of their respective earnings towards the total house rent. In the following month, the rent remains unchanged, while their earnings increase by 10%, 12% and 15%, respectively. What percentage of their combined earnings is spent on rent in the following month? Give the answer to the nearest 0.1%.

Answer and solution

Correct answer: C

Solution

Answer: C — 13.3%

1. Use earnings 8k,6k,5k. Rent=0.15(8k)+0.12(6k)+0.18(5k)=2.82k.

2. Next-month incomes are 8.8k,6.72k,5.75k. Their total is 21.27k.

3. The rent is unchanged, so its new share is (2.82/21.27)×100=13.2581…%.

4. Rounded to the nearest 0.1%, the answer is 13.3%, option C. Do not average the three individual contribution percentages.

Why this method works:
Percentages must be weighted by each person’s earnings. With incomes₹800,₹600,₹500, contributions are₹120,₹72,₹90. The same₹282 rent is then compared with the new total income, not the old₹1,900 total.

Independent check and common trap:
New incomes₹880,₹672,₹575 total₹2,127. The ratio 282/2127×100 is 13.2581…%, which rounds upward to 13.3% at one decimal. OptionB 13.2% is truncation rather than rounding; the original rent share 14.84% uses the wrong month.

G Strategy shortcut

Spot: Percentages.
Apply: Choose earnings 800,600,500. Rent=282 and new total=2127. Compute 282/2127×100≈13.258%, then round once to 13.3%.
Check: New incomes₹880,₹672,₹575 total₹2,127. The ratio 282/2127×100 is 13.2581…%, which rounds upward to 13.3% at one decimal. OptionB 13.2% is truncation rather than rounding; the original rent share 14.84% uses the wrong month.

G Strategy: Spot: Percentages. Apply: Choose earnings 800,600,500. Rent=282 and new total=2127. Compute 282/2127×100≈13.258%, then round once to 13.3%. Check: New incomes₹880,₹672,₹575 total₹2,127. The ratio 282/2127×100 is 13.2581…%, which rounds upward to 13.3% at one decimal. OptionB 13.2% is truncation rather than rounding; the original rent share 14.84% uses the wrong month.

Question 9Averages

TITA (type the answer) · +3 / 0 · easy

Four numbers are such that the mean of the first two exceeds the first number by 1; the mean of the first three exceeds the mean of the first two by 2; and the mean of all four exceeds the mean of the first three by 3. Find the difference between the largest and the smallest of the four numbers.

Your answer

Answer and solution

Correct answer: 15

Solution

Answer: 15

1. Let the first number be a. The mean of two numbers is a+1, so their sum is 2a+2 and the second number is a+2.

2. The mean of three is a+3, giving total 3a+9. Subtract 2a+2 to get third number a+7.

3. The mean of four is a+6, giving total 4a+24. Subtract 3a+9 to get fourth number a+15.

4. They increase in order a, a+2, a+7, a+15. Largest−smallest=15.

Why this method works:
An average is a total divided by a count. Whenever a new number is added, recover its value by subtracting the earlier total from the new total; the increase in the average is not itself the new number.

Independent check and common trap:
Setting the first number to 0 gives numbers 0,2,7,15. Their successive means are 1,3,6, with increments 1,2,3 as required. Adding any common constant shifts all numbers equally and leaves the range 15 unchanged.

G Strategy shortcut

Spot: Averages.
Apply: Shift the first number to 0 without changing the range. Running averages become 0,1,3,6; running totals 0,2,9,24. Differences give 0,2,7,15.
Check: Setting the first number to 0 gives numbers 0,2,7,15. Their successive means are 1,3,6, with increments 1,2,3 as required. Adding any common constant shifts all numbers equally and leaves the range 15 unchanged.

G Strategy: Spot: Averages. Apply: Shift the first number to 0 without changing the range. Running averages become 0,1,3,6; running totals 0,2,9,24. Differences give 0,2,7,15. Check: Setting the first number to 0 gives numbers 0,2,7,15. Their successive means are 1,3,6, with increments 1,2,3 as required. Adding any common constant shifts all numbers equally and leaves the range 15 unchanged.

Question 11Simple & Compound Interest

MCQ · +3 / −1 · easy

A sum of Rs 10,000 is deposited in Bank P for some number of years at 5% simple interest per annum. On maturity, the entire amount is transferred to Bank Q for a further 5 years at 6% simple interest per annum. If the interest earned in Bank P and Bank Q are in the ratio 10:13, for how many years was the money deposited in Bank P?

Answer and solution

Correct answer: C

Solution

Answer: C — 6 years

1. Let the first deposit duration be t years. Interest in P=10000×0.05t=500t.

2. The full maturity amount 10000+500t goes into Q. Five years at 6% simple interest earns 30% of this amount.

3. Thus Q interest=3000+150t. Use 500t/(3000+150t)=10/13.

4. 6500t=30000+1500t, so t=6. Check interests 3000 and 3900, ratio 10:13. Answer C.

Why this method works:
BankQ’s principal includes the original₹10,000 plus all interest from BankP. The second interest is therefore 30% of the maturity amount, not 30% of₹10,000. The ratio 10:13 compares interest amounts, not final balances.

Independent check and common trap:
For t=6, BankP earns₹3,000 and transfers₹13,000. BankQ earns 13,000×6%×5=₹3,900. Their ratio 3,000:3,900 reduces to 10:13, confirming both the time and the correct principal for the second stage.

G Strategy shortcut

Spot: Simple Interest.
Apply: Bank Q earns 30% of its starting amount. If Bank P interest is I, use I/[0.3(10000+I)]=10/13 to get I=3000, then 3000/500=6 years.
Check: For t=6, BankP earns₹3,000 and transfers₹13,000. BankQ earns 13,000×6%×5=₹3,900. Their ratio 3,000:3,900 reduces to 10:13, confirming both the time and the correct principal for the second stage.

G Strategy: Spot: Simple Interest. Apply: Bank Q earns 30% of its starting amount. If Bank P interest is I, use I/[0.3(10000+I)]=10/13 to get I=3000, then 3000/500=6 years. Check: For t=6, BankP earns₹3,000 and transfers₹13,000. BankQ earns 13,000×6%×5=₹3,900. Their ratio 3,000:3,900 reduces to 10:13, confirming both the time and the correct principal for the second stage.

Question 17Mixtures & Alligation

MCQ · +3 / −1 · easy

A container is full of milk. One-third of its contents is removed and replaced with water. The contents are mixed thoroughly before each removal. The same operation is repeated three more times. Find the final ratio of milk to water.

Answer and solution

Correct answer: B

Solution

Answer: B — 16:65

1. Assume the milk and water are uniformly mixed before each removal, as in standard replacement questions.

2. Each operation removes 1/3 of the milk currently present and retains 2/3. Replacing with water adds no milk.

3. Four operations leave (2/3)⁴=16/81 of the container as milk.

4. Water occupies 1−16/81=65/81. Hence milk: water=16:65, option B.

Why this method works:
Thorough mixing makes the fraction of milk removed equal to the fraction of the container removed. After each replacement the container is full again, so the same retention factor applies at every step rather than subtracting a fixed milk volume.

Independent check and common trap:
Taking capacity 81 units makes the sequence transparent: milk 81→54→36→24→16. The final water is 81−16=65. Four operations are required because the first operation is followed by three more; stopping after three would give 8:19.

G Strategy shortcut

Spot: Mixtures and Alligation.
Apply: One operation plus three MORE is four. Milk fraction=(2/3)⁴=16/81; water is its complement 65/81. Ratio 16:65.
Check: Taking capacity 81 units makes the sequence transparent: milk 81→54→36→24→16. The final water is 81−16=65. Four operations are required because the first operation is followed by three more; stopping after three would give 8:19.

G Strategy: Spot: Mixtures and Alligation. Apply: One operation plus three MORE is four. Milk fraction=(2/3)⁴=16/81; water is its complement 65/81. Ratio 16:65. Check: Taking capacity 81 units makes the sequence transparent: milk 81→54→36→24→16. The final water is 81−16=65. Four operations are required because the first operation is followed by three more; stopping after three would give 8:19.

Question 19Profit, Loss & Discount

MCQ · +3 / −1 · easy

An item is sold at a price that gives a 40% profit. If its cost had been 40% lower and it had been sold for Rs 5 less than the original selling price, the profit would have been 50%. Find the original selling price.

Answer and solution

Correct answer: B

Solution

Answer: B — Rs 14

1. Let original cost be C. At 40% profit the original selling price is 1.4C.

2. The reduced cost would be 0.6C. At 50% profit its selling price would be 1.5×0.6C=0.9C.

3. This hypothetical price is ₹5 below the original: 1.4C−0.9C=5. Hence C=10.

4. Original selling price=1.4×10=₹14, option B. Check new cost ₹6 and new SP ₹9 give 50% profit.

Why this method works:
Both profit percentages use their own cost prices. In the hypothetical case the cost is 60% of the original, so 50% profit makes the hypothetical selling price 90% of the original cost. It is not 50% above the original cost.

Independent check and common trap:
Original cost₹10 gives selling price₹14. The alternative cost₹6 gives selling price₹9, earning₹3 or 50% profit. The two selling prices differ by₹5, as required; the requested answer is₹14 rather than cost₹10.

G Strategy shortcut

Spot: Profit and Loss.
Apply: Old SP=140% of original CP. New SP=150% of 60%=90% of original CP. The 50% gap is ₹5, so CP=₹10 and SP=₹14.
Check: Original cost₹10 gives selling price₹14. The alternative cost₹6 gives selling price₹9, earning₹3 or 50% profit. The two selling prices differ by₹5, as required; the requested answer is₹14 rather than cost₹10.

G Strategy: Spot: Profit and Loss. Apply: Old SP=140% of original CP. New SP=150% of 60%=90% of original CP. The 50% gap is ₹5, so CP=₹10 and SP=₹14. Check: Original cost₹10 gives selling price₹14. The alternative cost₹6 gives selling price₹9, earning₹3 or 50% profit. The two selling prices differ by₹5, as required; the requested answer is₹14 rather than cost₹10.

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