The DAV Books Solutions Class 5 Maths and DAV Class 5 Maths Chapter 12 Brain Teasers Solutions of Percentage offer comprehensive answers to textbook questions.
DAV Class 5 Maths Ch 12 Brain Teasers Solutions
Question 1.
Tick (✓) the correct answer.
(a) 10% of 74.6 is-
(i) 4.6
(ii) 7.4
(iii) 7.46
(iv) 746
Solution:
\(\frac{10}{100}\) of 74.6 = \(\frac{10}{100}\) × 74.6 = 7.46
So, option (iii) is correct.
(b) 8 tenths = ______%
(i) 8
(ii) 80
(iii) 0.8
(iv) 0.08
Solution:
8 tenth = (\(\frac{8}{10}\) × 100)% = 80%
So, option (ii) is correct.
(c) 33\(\frac{1}{3}\)% of 10% of 600 litres = ______ litres.
(i) 20
(ii) 120
(iii) 200
(iv) 220
Solution:
33\(\frac{1}{3}\)% of 10% of 600 l
= \(\frac{100}{3}\)% × 10% × 600 l
= \(\frac{100}{3} \times \frac{1}{100} \times \frac{10}{100}\) × 600 l
= 20 l
So, option (i) is correct.
(d) The percentage of shaded part in the given figure is-
(i) 80%
(ii) 70%
(iii) 75%
(iv) 85%
Solution:
\(\frac{3}{4}\) = (\(\frac{3}{4}\) × 100)% = 75%
So, option (iii) is correct.
(e) Jack went up the hill and came down with a bucket three-fifth filled with water. Then the percentage of water left to be filled in the bucket is-
(i) 60%
(ii) 30%
(iii) 40%
(iv) 50%
Solution:
\(\frac{3}{5}\) = (\(\frac{3}{5}\) × 100)%
= (3 × 20)%
= 60%
% of water left to be filled = (100 – 60)% = 40%
So, option (iii) is correct.
Question 2.
Write each of the following as a percentage.
(a) 7 tenths
Solution:
7 tenths = (\(\frac{7}{10}\) × 100)% = 70%
(b) \(\frac{328}{100}\)
Solution:
\(\frac{328}{100}\) = (\(\frac{328}{100}\) × 100)% = 328%
(c) 0.07
Solution:
0.07 = (\(\frac{0.07}{100}\) × 100)% = 7%
(d) 5\(\frac{1}{5}\)
Solution:
5\(\frac{1}{5}\) = \(\frac{26}{5}\)
= (\(\frac{26}{5}\) × 100)%
= 520%
Question 3.
Express as a fraction in the lowest term.
(a) 35%
Solution:
35% = \(\frac{35}{100}\) = \(\frac{7}{20}\)
(b) 16\(\frac{2}{3}\)%
Solution:
16\(\frac{2}{3}\)% = \(\frac{50}{3 \times 100}\) = \(\frac{1}{6}\)
(c) 2\(\frac{3}{4}\)%
Solution:
2\(\frac{3}{4}\)% = \(\frac{11}{4} \times \frac{1}{100}\) = \(\frac{11}{400}\)
(d) 90%
Solution:
90% = \(\frac{90}{100}\) = \(\frac{9}{10}\)
Question 4.
Express as a decimal.
(a) 71%
Solution:
71% = \(\frac{71}{100}\) = 0.71
(b) 9.5%
Solution:
9.5% = \(\frac{9.5}{100}\) = 0.095
(c) 101%
Solution:
101% = \(\frac{101}{100}\) = 1.01
(d) 759%
Solution:
759% = \(\frac{759}{100}\) = 7.59
Question 5.
Find the value of-
(a) 33\(\frac{1}{3}\)% of 429 metres
Solution:
33\(\frac{1}{3}\)% of 429 metres
= \(\frac{100}{3 \times 100}\) × 429
= 143 m
(b) 50% of 4 metres
Solution:
50% of 4 metres
= \(\frac{50}{100}\) × 4
= 2 m
(c) 100% of 200 grams
Solution:
100% of 200 grams
= \(\frac{100}{100}\) × 200
= 200 gm
(d) 20% of 1 kg
Solution:
20% of 1 kg
= \(\frac{20}{100}\) × 1
= \(\frac{1}{5}\)
= 0.2 kg or 200 gms
(e) 6\(\frac{1}{4}\)% of 1 litre
Solution:
6\(\frac{1}{4}\)% of 1 litre
= \(\frac{25}{4 \times 100}\) × 1
= \(\frac{1}{16}\) l
= 0.0625 l
(f) 12\(\frac{1}{2}\)% of ₹ 32
Solution:
12\(\frac{1}{2}\)% of ₹ 32
= \(\frac{25}{2 \times 100}\) × 32
= ₹ 4
Question 6.
A school contributed ₹ 3,500 to the flood relief fund. Sonal donated 10% of the fund. How much money was donated by Sonal?
Solution:
Total contribution of school = ₹ 3,500
Sonal’s contribution = 10%
Money contribution of Sonal = \(\frac{10}{100}\) × 3500 = ₹ 350
The money donated by Sonal was ₹ 350.
Question 7.
Mr Arun earns ₹ 35,500 per month. He spends 70% on household expenses, 25% on children, and saves the rest. How much money did Arun save?
Solution:
Earning of Mr Aran per month = ₹ 35,500
His expenditure = 70% + 25% = 95%
Saves = (100 – 95)% = 5%
His savings = \(\frac{5}{100}\) × 35500 = ₹ 1,775
Arun saved ₹ 1,775.
Question 8.
Mr Gupta took his family out for dinner. The amount of the bill was ₹ 875. Mr Gupta paid 5% of the bill amount as a tip. Find the money given as a tip.
Solution:
Amount of bill = ₹ 875
% of tip = 5%
Money as tip = 5% of ₹ 875
Amount paid at tip = \(\frac{5}{100}\) × 875 = ₹ 43.75
The money given as tip is ₹ 43.75.
Question 9.
Find the percentage of the letter ‘M’ in the word MATHEMATICS.
Solution:
Total alphabets = 11
% of ‘M’ = (\(\frac{2}{11}\) × 100)%
= (\(\frac{200}{11}\))%
= 18\(\frac{2}{11}\)%
Question 10.
Some numbers are below:
5, 2, 18, 26, 31, 42, 65, 7, 13, 35
Find the percentage of:
(a) Even numbers
(b) Odd numbers
(c) Prime numbers
(d) Odd primes
(e) Multiples of 5
(f) Even primes
Solution:
(a) Total numbers = 10
Even numbers = 4
% of even numbers = (\(\frac{4}{10}\) × 100)% = 40%
(b) Total numbers = 10
Odd numbers = 6
% of odd numbers = (\(\frac{6}{10}\) × 100)% = 60%
(c) Total number = 10
Prime numbers = 5
% of prime numbers = (\(\frac{5}{10}\) × 100)%
(d) Total numbers = 10
Odd prime numbers = 4
% of odd primes = (\(\frac{4}{10}\) × 100)% = 40%
(e) Total numbers = 10
Multiples of 5 = 3
% of multiples of 5 = (\(\frac{3}{10}\) × 100)% = 30%
(f) Total numbers = 10
Even primes = 1
% of even primes = (\(\frac{1}{10}\) × 100)% = 10%
Additional Questions
Question 1.
Complete the following:
(a)
Solution:
\(\frac{22}{100}\) = 22%
(b)
Solution:
\(\frac{133}{100}\) = 133%
(c)
Solution:
\(\frac{46}{100}\) = 46%
(d)
Solution:
\(\frac{89}{100}\) = 89%
(e)
Solution:
\(\frac{56}{100}\) = 56%
Question 2.
Convert the following percentages into fractions in the lowest term:
(a) 45%
Solution:
45% = \(\frac{45}{100}\) = \(\frac{9}{20}\)
(b) 125%
Solution:
125% = \(\frac{125}{100}\)
= \(\frac{5}{4}\)
= 1\(\frac{1}{4}\)
(c) 176%
Solution:
176% = \(\frac{176}{100}\)
= \(\frac{44}{25}\)
= 1\(\frac{19}{25}\)
(d) 89%
Solution:
89% = \(\frac{89}{100}\)
Question 3.
Express the following percentages into decimals:
(a) 8.8%
Solution:
8.8% = \(\frac{8.8}{100}\) = 0.088
(b) 8.9%
Solution:
8.9% = \(\frac{8.9}{100}\) = 0.089
(c) 2.9%
Solution:
2.9% = \(\frac{2.9}{100}\) = 0.029
(d) 0.38%
Solution:
0.38% = \(\frac{0.38}{100}\) = 0.0038
Question 4.
Convert the following into percentages.
(a) \(\frac{8}{25}\)
Solution:
\(\frac{8}{25}\) = (\(\frac{8}{25}\) × 100)% = 32%
(b) 3\(\frac{1}{4}\)
Solution:
3\(\frac{1}{4}\) = (\(\frac{13}{4}\) × 100)%
= (13 × 25)%
= 325%
Question 5.
Convert the following into percentages.
(a) 0.732
Solution:
0.732 = (0.732 × 100)% = 73.2%
(b) 3.7
Solution:
3.7 = (3.7 × 100)% = 370%
(c) 31.87
Solution:
31.87 = (31.87 × 100)% = 3187%
(d) 41.35
Solution:
41.35 = (41.35 × 100)% = 4135%
Question 6.
Find
(a) 20% of 800
Solution:
20% of 800 = \(\frac{20}{100}\) × 800 = 160
(b) 2\(\frac{1}{4}\)% of 160
Solution:
2\(\frac{1}{4}\)% of 160 = \(\frac{9}{4}\) × \(\frac{1}{100}\) × 160 = 3.6
(c) 2% of 400
Solution:
2% of 400 = \(\frac{2}{100}\) × 400 = 8