Mathematics Problem Solving

In a test, Charan secured 54 marks that was also equivalent to obtaining 72% marks. How many marks was the test out of?

• 75

• 85

• 80

• 65

Answer explanation

Charan scored 54 marks, which is 72% of the total marks. To find the total marks, use the formula: Total Marks = (Marks Obtained / Percentage) x 100. Thus, Total Marks = (54 / 72) x 100 = 75. Therefore, the test was out of 75.

Ramu used to spend 72% of his income. His income is increased by 12% and he increases his expenditure by 5%. If Ramu earlier saved `y and after the increases he now saves `x, then what is the value of (x-y) ×100%/y?

• 30%

• 22%

• 25%

• 27%

Answer explanation

Ramu's initial savings are 28% of his income. After a 12% income increase, his new income is 112%. With a 5% increase in expenditure, he spends 77.6%. His new savings are 34.4%. Thus, (34.4-28)×100%/28 = 30%. Hence, the answer is 30%.

The income of Raman is `45,000. He saves 12.5% of his income. If his income increases by 18% and expenditure increases by 20%, then his savings will:

• decrease by `215

• increase by `225

• increase by `250

• decrease by `220

Answer explanation

Raman's initial savings are 12.5% of 45,000, which is 5,625. After an 18% income increase, his income is 53,100. With a 20% expenditure increase, his savings rise to 5,850. The increase in savings is 225, confirming the correct choice.

A man saves 30% of his monthly income. If his monthly income increases by 10%, then he saves 20% more than the previous savings. The percentage increase in his expenditure is _____ (rounded off to one decimal place).

• 5.7%

• 4.8%

• 7.3%

• 6.8%

Answer explanation

Let the initial income be 100. Savings = 30. New income = 110, new savings = 36. Savings increase = 6. Expenditure = income - savings = 70. New expenditure = 110 - 36 = 74. Percentage increase in expenditure = (4/70)*100 = 5.7%.

Tanvi saves `5,000 from the salary every month after spending 80% of her monthly salary. Tanvi's salary is:

• `25,000

• `30,000

• `35,000

• `20,000

Answer explanation

Tanvi saves 5,000 after spending 80% of her salary. Let her salary be x. Then, 20% of x = 5,000. So, x = 5,000 / 0.2 = 25,000. Thus, Tanvi's salary is `25,000.

From the salary of Hari, 15% is deducted as house rent, 20% of the remaining amount is spent on children's education and 10% of the remaining balance is his medical expenses, Finally, he is left with `42,840. Find his total salary.

• `65,000

• `75,000

• `72,000

• `70,000

Answer explanation

Let Hari's salary be x. After 15% deduction, he has 0.85x. Spending 20% on education leaves 0.8 * 0.85x = 0.68x. After 10% medical expenses, he has 0.9 * 0.68x = 0.612x. Setting 0.612x = 42840 gives x = 70000.

Last year, Ranjan's monthly salary was Rs. 34,500 and this year his monthly salary is Rs. 38,640. What is the percentage increase in Ranjan's monthly salary in this year over his monthly salary last year?

• 15%

• 12%

• 20%

• 13%

Answer explanation

To find the percentage increase, use the formula: ((New Salary - Old Salary) / Old Salary) * 100. Here, ((38640 - 34500) / 34500) * 100 = (4140 / 34500) * 100 ≈ 12%. Thus, the correct answer is 12%.

Vikas spends 80% of his salary. His salary is increased by 25% and his expenditure increased by 15%. What is the percentage increase in his savings?

• 55%

• 50%

• 60%

• 65%

Answer explanation

Let Vikas's salary be S. His initial savings = S - 0.8S = 0.2S. After a 25% increase, salary = 1.25S. Expenditure after 15% increase = 0.8S * 1.15 = 0.92S. New savings = 1.25S - 0.92S = 0.33S. Percentage increase in savings = (0.33S - 0.2S) / 0.2S * 100 = 65%.

The sum of the salaries of A and B together is `4300. A spends 95% of his salary and B, 80% of his salary. If their savings are the same, what is A's salary?

• `3442

• `3430

• `3440

• `3445

Answer explanation

Let A's salary be x. Then B's salary is 4300 - x. A saves 5% of x and B saves 20% of (4300 - x). Setting these equal gives 0.05x = 0.2(4300 - x). Solving this, we find x = 3440. Thus, A's salary is `3440.

Ravi's salary is 20% more than Mohan's salary. If Mohan's salary is `1600 then Ravi's salary will be:

• `1890

• `1920

• `800

• `1750

Answer explanation

Ravi's salary is 20% more than Mohan's. Mohan's salary is `1600, so Ravi's salary = 1600 + (20/100 * 1600) = 1600 + 320 = `1920. Thus, the correct answer is `1920.