Percentages Formulas

Question 1 : Peaches are now 50% more expensive at Reliance Smart Point. What percentage reduction in consumption is required to maintain peach expenditure constant?

1. 35 %
2. 35.50 %
3. 33.33 %
4. 32.50 %

Answer: 3.

Explanation:
If the price of a commodity increases by r%, then the reduction in consumption so as not to increase the expenditure is –

(\frac{r}{100+r}\times 100)%

Therefore r is the increased price(i.e 50)

By using the formula:
(\frac{50}{100+50}\times 100)%=\frac{50}{150}\times100=33.33 %

Question2 : Jason Statham could set aside 10% of his earnings. However, when his income increased by 20% two years later, he could only save the same amount as before. How much has his spending increased by percentage?

1. 22\frac{2}{9}%
2. 21\frac{5}{7}%
3. 22\frac{2}{8}%
4. 23\frac{1}{9}%

Answer: 1.

Explanation:
Let earlier income be 100 Rs
∴ Savings = 10% of 100 = 10 Rs
∴ Expenditure = 90 Rs

New Income = 120 Rs

Savings (same as before) = 10 Rs

∴ Expenditure = 120 – 10 = 110 Rs

∴ Increase in Expenditure = 110 – 90 = 20

Percentage Increase= \frac{20}{90}\times 100%=22\frac{2}{9}%

Question 3 : To pass the NDA Recruitment Test, candidates must receive 290 of the aggregate marks to pass. What is the highest total of marks an applicant can receive if they receive 203 and are considered unsuccessful by 12% of their total scores?

1. 750
2. 725
3. 700
4. 675

Answer: 2.

Explanation:
Let’s maximum aggregate marks = x

203 + 12% of x = 290

12% of x = 290 – 203

x=\frac{87\times100}{12}=725.

Question 4: 12. Robert Pattinson is an IT professional who spends 12% of his monthly income on power, 25% of his income on food, 20% of his income on his children’s education, 30% of his income on rent, and the rest 1040 on everything else. What is the person’s monthly salary?

1. 7500 Rs
2. 7700 Rs
3. 7900 Rs
4. 8000 Rs

Answer:4.

Explanation:
Let the monthly salary of the Robert be x. then,

Total spends of Robert = (30 + 25 + 20 + 12) = 87%

Remaining % = 100 – 87 = 13%
So, 13% ≡ 1040

100% ≡ x
Using the cross multiplication method,
x=\frac{1040\times100}{13}=80\times 100= 8000 Rs

Question 5 : If Yasir’s income is 20% less than Xavier’s, by what percentage does Yasir’s salary fall short of Xavier’s?

1. 16.66 %
2. 15.50 %
3. 14.45 %
4. 13.45 %

Answer: 1.

Explanation:
Let the salary of Yasir be 100. then,

Salary of Xavier will be 120.

Yasir less than Xavier in %,

=\frac{120-100}{120}\times 100=\frac{20}{120}\times 100=16.33 %