Arithmetic — Practice

Question 1

In a survey of 90 people, 36 preferred brand X. What percentage preferred brand X?

Accepted Answer

$\frac{36}{90}	imes100=40\%$.

Answer: 40%.

Question 2

45 is what percentage of 180?

Accepted Answer

$\frac{45}{180}	imes100=25\%$.

Answer: 25%.

Question 3

A trader buys an item for ₹340 and sells it for ₹425. Find the profit percentage.

Accepted Answer

Profit $=425-340=85$. Profit \% $=\frac{85}{340}	imes100=25\%$.

Answer: 25%.

Question 4

The average of 9 numbers is 48. Find their sum.

Accepted Answer

Sum $=48	imes9=432$.

Answer: 432.

Question 5

An item bought for ₹600 is sold for ₹510. Find the loss percentage.

Accepted Answer

Loss $=600-510=90$. Loss \% $=\frac{90}{600}	imes100=15\%$ (loss percent divides by cost price too).

Answer: 15%.

Question 6

A person earns ₹32,000 a month and spends ₹24,000. Find their savings percentage.

Accepted Answer

Savings $=32000-24000=8000$. Savings \% $=\frac{8000}{32000}	imes100=25\%$.

Answer: 25%.

Question 7

A shop's daily footfall increased from 350 to 420 customers. Find the percentage increase.

Accepted Answer

$\frac{420-350}{350}	imes100=\frac{70}{350}	imes100=20\%$.

Answer: 20%.

Question 8

Which ratio is larger: 5:6 or 8:9?

Accepted Answer

$\frac{5}{6}\approx0.833$ and $\frac{8}{9}\approx0.889$. Since $0.889>0.833$, the ratio 8:9 is larger.

Answer: 8:9 is larger.

Question 9

In a two-candidate election, the winner received 55% of the total votes and won by a margin of 1,200 votes. Find the total number of votes cast.

Accepted Answer

The margin represents $55\%-45\%=10\%$ of the total. Total $=1200\div0.10=12{,}000$.

Answer: 12,000 votes.

Question 10

A sum is divided among A, B and C in the ratio 4:6:9. If C receives ₹1,500 more than A, find the total sum.

Accepted Answer

C and A's ratio terms differ by $9-4=5$ parts, corresponding to ₹1,500, so one part $=1500\div5=₹300$. Total parts $=4+6+9=19$, so the total sum is $300	imes19=₹5{,}700$.

Answer: ₹5,700.

Question 11

The average of 7 numbers is 30. When an 8th number is included, the average of all 8 becomes 33. Find the 8th number.

Accepted Answer

Old sum $=7	imes30=210$. New sum $=8	imes33=264$. Included number $=264-210=54$.

Answer: 54.

Question 12

One group of 18 students has an average score of 65, and a second group of 22 students has an average score of 75. Find the combined average of all 40 students.

Accepted Answer

Combined sum $=18	imes65+22	imes75=1170+1650=2820$. Combined average $=\frac{2820}{40}=70.5$.

Answer: 70.5.

Practice — Arithmetic

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