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Shortcut Trick

Assume Total Investment is 6 units.

Taru investment = 1/6 × 6 = 1 unit.

Remaining investment = 6 − 1 = 5 units, divided equally between Anu and Daksh.

Anu = 2.5 units, Daksh = 2.5 units.

Difference between Taru and Daksh = 2.5 − 1 = 1.5 units.

Profit difference = (1.5 ÷ 6) × 7200 = 1800.

∴ The correct answer is Rs. 1800.

Alternate Method

Given: Total Profit = Rs. 7200, Taru investment = 1/6 of Total, Anu = Daksh.

Formula: Profit Share ∝ Investment × Time period.

⇒ Let Total Investment be x. Taru = x/6.

⇒ Anu + Daksh = x − x/6 = 5x/6.

⇒ Since Anu = Daksh, each invested (5x/6) ÷ 2 = 5x/12.

⇒ Ratio of Profit (Taru : Anu : Daksh) = 1/6 : 5/12 : 5/12 = 2 : 5 : 5.

⇒ Taru Profit = (2/12) × 7200 = 1200.

⇒ Daksh Profit = (5/12) × 7200 = 3000.

⇒ Difference = 3000 − 1200 = 1800.

∴ The correct answer is Rs. 1800.

Additional Information

Partnership Profit Distribution

Profit is divided in the ratio of the product of Capital and Time. If time is constant, Profit Ratio = Capital Ratio.

Ratio Balancing

To simplify fractions like 1/6 and 5/12, multiply all terms by the LCM of denominators (12) to get whole numbers.

Shortcut Trick

Ratio of Ranjan : Sanjay = 3 : 2.

Difference in ratio parts = 3 − 2 = 1 unit.

Age difference = 8 + 8 = 16 years.

1 unit = 16 years ⇒ Sanjay (2 units) = 32 years.

Irfan = 32 + 12 = 44 years.

∴ The correct answer is 44 years.

Alternate Method

Given: Ratio of ages = 3 : 2; Irfan = Sanjay + 12.

Formula: Age after n years = Age + n; Age n years ago = Age − n.

⇒ Let Ranjan = 3x and Sanjay = 2x.

⇒ According to question: 2x + 8 = 3x − 8

⇒ 3x − 2x = 8 + 8

⇒ x = 16

⇒ Sanjay present age = 2 × 16 = 32 years.

⇒ Irfan present age = 32 + 12 = 44 years.

∴ The correct answer is 44 years.

Additional Information

Age Difference Invariability

The difference between the ages of two persons remains constant throughout their lives regardless of the number of years passed.

Ratio and Proportion in Ages

If the ratio of ages is a : b, their actual ages can be assumed as ax and bx. The value of x is found using the given linear conditions.

Shortcut Trick

Difference in salary ratio parts = 21 − 20 = 1 unit.

Given 1 unit = ₹2000 ⇒ Salary of P = 20 × 2000 = ₹40,000; Salary of Q = 21 × 2000 = ₹42,000.

Expenditure of Q = Salary − Savings = 42,000 − 14,000 = ₹28,000.

Expenditure ratio P:Q is 5:7 → 7 units = 28,000 ⇒ 5 units (P) = ₹20,000.

Savings of P = 40,000 − 20,000 = ₹20,000.

Savings Ratio P:Q = 20,000 : 14,000 = 10 : 7.

∴ The correct answer is 10 : 7.

Alternate Method

Given: Salary ratio P:Q = 20:21, Expenditure ratio P:Q = 5:7.

Formula: Savings = Income − Expenditure

⇒ Let Salary of P = 20x and Q = 21x.

⇒ Difference = 21x − 20x = x = ₹2000.

⇒ Salary P = 20 × 2000 = ₹40,000; Salary Q = 21 × 2000 = ₹42,000.

⇒ Expenditure of Q = Salary Q − Savings Q = 42,000 − 14,000 = ₹28,000.

⇒ Let Expenditure of P = 5y and Q = 7y. Since 7y = 28,000 ⇒ y = 4,000.

⇒ Expenditure of P = 5 × 4,000 = ₹20,000.

⇒ Savings of P = 40,000 − 20,000 = ₹20,000.

⇒ Required Ratio = Savings P : Savings Q = 20,000 : 14,000 = 10 : 7.

∴ The correct answer is 10 : 7.

Additional Information

Income and Savings Relation

Income = Expenditure + Savings. If any two variables are known or their ratios are provided with a fixed difference, the third can be calculated.

Ratio and Proportion

If a:b is the ratio and the difference between quantities is d, then the actual values are [a/(b−a)]×d and [b/(b−a)]×d.

Cross Multiplication Method

Used when initial ratio, changes (savings), and final ratio (expenditure) are given: (Initial Ratio × Final Ratio parts) − (Savings × Ratio parts).

Shortcut Trick

Equate the total sum of ratios: Original (3+4+5 = 12) and New (9+4+7 = 20).

LCM of 12 and 20 is 60. Multiply Original ratio by 5 and New ratio by 3.

Original B = 4 × 5 = 20 units; New B = 4 × 3 = 12 units.

Difference in B = 20 − 12 = 8 units → ₹60. Total amount (60 units) = (60/8) × 60 = ₹450.

∴ The correct answer is ₹450.

Alternate Method

Given: Original ratio A:B:C = 3:4:5 | New ratio A:B:C = 9:4:7 | Loss for B = ₹60

Formula: Share = (Individual Ratio / Total Ratio) × Total Amount (X)

⇒ Original share of B = (4 / (3+4+5)) × X = 4X / 12 = X / 3

⇒ New share of B = (4 / (9+4+7)) × X = 4X / 20 = X / 5

⇒ Difference = (X / 3) − (X / 5) = 60

⇒ (5X − 3X) / 15 = 60

⇒ 2X / 15 = 60

⇒ 2X = 900

⇒ X = 450

∴ The correct answer is ₹450.

Additional Information

Ratio Balancing

When the total quantity remains constant across two different ratio distributions, multiply each ratio by the total sum of the other ratio to balance them.

Compound Ratio

The compound ratio of (a : b) and (c : d) is (ac : bd), used when multiple factors influence a final share.

Inverse Ratio Property

If an amount is distributed inversely to original values, the new share of x is proportional to 1/x.

Shortcut Trick

Let Cost Price (CP) = 100 units. Marked Price (MP) = 140 units.

Difference in Discount = 15% − 10% = 5% of MP.

5% of 140 = 7 units. Given, 7 units = Rs. 21 ⇒ 1 unit = Rs. 3.

For 20% discount: Selling Price (SP) = 140 × 80/100 = 112 units.

Profit = 112 − 100 = 12 units ⇒ 12 × 3 = Rs. 36.

∴ The correct answer is Rs. 36.

Alternate Method

Given: Markup = 40%, D₁ = 10%, D₂ = 15%, Profit Decrease = Rs. 21.

Formulas: MP = CP × (100 + Markup%) ÷ 100 | SP = MP × (100 − D%) ÷ 100 | Profit = SP − CP

⇒ Let CP = x. Then MP = 1.4x.

⇒ Case 1 SP = 1.4x × 0.9 = 1.26x. Case 2 SP = 1.4x × 0.85 = 1.19x.

⇒ Difference in Profit = 1.26x − 1.19x = 0.07x.

⇒ 0.07x = 21 ⇒ x = 21 ÷ 0.07 = 300.

⇒ For 20% discount: SP = 1.4 × 300 × 0.8 = 336.

⇒ Profit = 336 − 300 = Rs. 36.

∴ The correct answer is Rs. 36.

Additional Information

Marked Price & Markup

Markup is the extra price added to the CP to arrive at MP. Markup% = (MP − CP) ÷ CP × 100.

Relation between CP and MP

CP ÷ MP = (100 − Discount%) ÷ (100 + Profit%). This ratio is very useful when both D% and P% are given.

Six people P, Q, R, S, T, and U

six different places Jaipur, Nagpur, Bangalore, Mumbai, Agra, and Delhi

1- P visited to Agra on 3^rd February and Only one person visited between P and the one who visited to Nagpur.

3- T visited immediately after the one who visited to Nagpur.

4- One person visited between T and U, who doesn't visited to Mumbai.

5- The one who visited Bangalore visited immediately after the one who visited to Mumbai.

6- S visited in a month of having 31 days but not in january and S doesn't visited on date 7 of any month.

7- Three people visited between S and R.

8- Only one person visited between the one who visited to Bangalore and the one who visited to Delhi.

9- Q doesn't visited immeediate after R. So case-2 gets eliminated.

So, Final arrangement is;

 

 

 

Hence, S visited Mumbai.

Six people P, Q, R, S, T, and U

six different places Jaipur, Nagpur, Bangalore, Mumbai, Agra, and Delhi

1- P visited to Agra on 3^rd February and Only one person visited between P and the one who visited to Nagpur.

3- T visited immediately after the one who visited to Nagpur.

4- One person visited between T and U, who doesn't visited to Mumbai.

5- The one who visited Bangalore visited immediately after the one who visited to Mumbai.

6- S visited in a month of having 31 days but not in january and S doesn't visited on date 7 of any month.

7- Three people visited between S and R.

8- Only one person visited between the one who visited to Bangalore and the one who visited to Delhi.

9- Q doesn't visited immeediate after R. So case-2 gets eliminated.

So, Final arrangement is;

 

 

Hence**, T who visited to Jaipur visited on 7^th January.**

Six people P, Q, R, S, T, and U

six different places Jaipur, Nagpur, Bangalore, Mumbai, Agra, and Delhi

1- P visited to Agra on 3^rd February and Only one person visited between P and the one who visited to Nagpur.

3- T visited immediately after the one who visited to Nagpur.

4- One person visited between T and U, who doesn't visited to Mumbai.

5- The one who visited Bangalore visited immediately after the one who visited to Mumbai.

6- S visited in a month of having 31 days but not in january and S doesn't visited on date 7 of any month.

7- Three people visited between S and R.

8- Only one person visited between the one who visited to Bangalore and the one who visited to Delhi.

9- Q doesn't visited immeediate after R. So case-2 gets eliminated.

So, Final arrangement is;

 

 

Hence, Two people visited between the one who visited to Agra and Q.

Six people P, Q, R, S, T, and U

six different places Jaipur, Nagpur, Bangalore, Mumbai, Agra, and Delhi

1- P visited to Agra on 3^rd February and Only one person visited between P and the one who visited to Nagpur.

3- T visited immediately after the one who visited to Nagpur.

4- One person visited between T and U, who doesn't visited to Mumbai.

5- The one who visited Bangalore visited immediately after the one who visited to Mumbai.

6- S visited in a month of having 31 days but not in january and S doesn't visited on date 7 of any month.

7- Three people visited between S and R.

8- Only one person visited between the one who visited to Bangalore and the one who visited to Delhi.

9- Q doesn't visited immeediate after R. So case-2 gets eliminated.

So, Final arrangement is;

 

 

Hence, U visited to Delhi.

Six people P, Q, R, S, T, and U

six different places Jaipur, Nagpur, Bangalore, Mumbai, Agra, and Delhi

1- P visited to Agra on 3^rd February and Only one person visited between P and the one who visited to Nagpur.

3- T visited immediately after the one who visited to Nagpur.

4- One person visited between T and U, who doesn't visited to Mumbai.

5- The one who visited Bangalore visited immediately after the one who visited to Mumbai.

6- S visited in a month of having 31 days but not in january and S doesn't visited on date 7 of any month.

7- Three people visited between S and R.

8- Only one person visited between the one who visited to Bangalore and the one who visited to Delhi.

9- Q doesn't visited immeediate after R. So case-2 gets eliminated.

So, Final arrangement is;

 

 

Hence, Q visited in the last.