Class 8 RD Sharma Solutions - Chapter 12 Percentage - Exercise 12.2 | Set 2

Chapter 12 Percentage - Exercise 12.2 | Set 1

Question 14. An alloy of tin and copper consists of 15 parts of tin and 105 parts of copper. Find the percentage of copper in the alloy?

Solution:

Given, number of Tin parts = 15 

The number of Copper parts = 105

So, total parts = 105 + 15 = 120

So, the percentage of Copper part = (105/120) × 100 = 87.5%

Hence, the percentage of Copper in an alloy is 87.5%

Question 15. An alloy contains 32% copper, 40% nickel and rest zinc. Find the mass of the zinc in 1 kg of the alloy.

Solution:

Given, the percentage of copper = 32 %

The percentage of nickel; = 40 %

So, the percentage of Zinc = 100 % -(32 % + 40 %) = 28 %

So, we can say the mass of zinc in 1 kg alloy = 28 % of 1 kg or 1000 gm

= (28/100) × 1000 = 280 grams

Hence, the mass of Zinc in 1 kg alloy is 280 gm

Question 16. A motorist travelled 122 kilometers before his first stop. If he had 10%of his journey to complete at this point, how long was the total ride?

Solution:

Given, the distance travelled by motorist before stopping = 122 km

Let a km be the total length of the whole journey

So, 10 % of a = 122 km

(10/100) × a = 122

a = 1220 km 

Hence, the length of the whole journey is 1220 km 

Question 17. A certain school has 300 students, 142 of whom are boys. It has 30 teachers, 12 of whom are men. What per cent of the total number of students and teachers in the school is female?

Solution:

Given, Total students = 300 

Total number of boys = 142

So, the number of girls = 300 – 142 = 158

Total number of teachers = 30

Number of male teachers = 12

So, the number of female teachers = 30 – 12 = 18

So, total number of females are = 158 + 18 = 176 

And total number of teachers and student = 300 + 30 = 330

So, the total percentage of females in school = (176/330) × 100 

= 53.33 %

Hence, the total percentage of females in school is 53.33%

Question 18. Aman’s income is 20% less than that of Anil. How much percent is Anil’s income more than Aman’s income?

Solution:

Let us take Rs 100 be the income of Anil

So, Aman income is 20% less than that of Anil's income 

i.e 100 – 20 = Rs 80

The difference in income of both Aman and Anil = Rs 100 - Rs 80 = Rs 20

So, Anil's income is Rs 20 more than Aman's income 

And in percentage it will be (20/80) × 100 = 25 %

Hence, Anil's income is 25% more than that of Aman's income

Question 19. The value of a machine depreciates every year by 5%. If the present value of the machine be Rs 100000, what will be its value after 2 years?

Solution:

Given, the present value of machine = Rs 100000

Also, every year the value of machine depreciates by 5 %

So, we can say that the value of machine after 2 years will be 100000 × (100-5)/100 × (100-5)/100

= 100000 × 95/100 × 95/100

= Rs 90250

Hence, the value of machine after 2 years will be Rs 90250

Question 20. The population of a town increases by 10% annually. If the present population is 60000, what will be its population after 2 years?

Solution:

Given, the present population of town = 60000

Also, every year the population of town increases by 10 %

So, we can say that the population of town after 2 years will be 60000 × (100+10)/100 × (100+10)/100

= 60000 × 110/100 × 110/100

= 72600

Hence, the population of town after 2 years will be 72600

Question 21. The population of a town increases by 10% annually. If the present population is 22000, find its population a year ago.

Solution:

Given, the present population of town = 22000

Also, every year the population of town increases by 10 %

Let a be the population of town a year ago

So, according to this the present population will be a × (100+10)/100

So, 22000 = 11a/10

a = 20000

Hence, the population of town a year ago is 20000

Question 22. Ankit was given an increment of 10% on his salary. His new salary is Rs. 3575. What was his salary before increment?

Solution:

Given, Ankit has an increment of 10% on his salary

His new salary is Rs. 3575

Let a be the original salary of Ankit

So, according to this his salary after increment will be a × (100+10)/100

So, 3575 = 11a/10

a = Rs 3250

Hence, the salary of Ankit before increment is Rs 3250

Question 23. In the new budget, the price of petrol rose by 10%. By how much percent must one reduce the consumption so that the expenditure does not increase?

Solution:

Given, the price of petrol rose by 10%

Reduction in the consumption so that the expenditure does not increase,

= (increase%)/(100 + increase%) × 100

= 10/(100+10) × 100

= 9.09 %

Hence, one can reduce the consumption of expenditure by 9.09%

Question 24. Mohan’s income is Rs 15500 per month. He saves 11% of his income. If his income increases by 10%, then he reduces his saving by 1%, how much does he save now?

Solution:

Given, Mohan income is Rs 15500

He saves 11% of his income

So, the savings of Mohan = 11% of Rs 15500

= (11/100) × 15500 

= Rs 1705

If his income increases by 10%, then new income 15500 + 10% of Rs 15500

= 15500 + (10/100) × 15500 

= Rs 17050

Also, he reduces his saving by 1%, so now he saves 11 – 1 = 10 % of his income

= 10% of Rs 17050

= Rs 1705

Hence, the savings of Mohan will remain the same i.e Rs 1705

Question 25. Shikha’s income is 60% more than that of Shalu. What percent is Shalu’s income less than Shikha’s?

Solution:

Let us take Rs 100 be the income of Shalu

So, Shikha income is 60% more than that of Shalu's income 

i.e 100 + 60 = Rs 160

The difference in income of both Shikha and Shalu = Rs 160 - Rs 100 = Rs 60

So, Shalu's income is Rs 60 less than Shikha's income 

And in percentage it will be (60/160) × 100 = 37.5%

Hence, Shalu's income is 37.5% less than that of Shikha's income

Question 26. Rs 3500 is to be shared among three people so that the first person gets 50% of the second, who in turn gets 50% of the third. How much will each of them get?

Solution:

Let third person will get Rs a

So, second person will get 50% of the third i.e (50/100) × a = a/2

Also, first person will get 50% of the second i.e (50/100) × a/2 = a/4

Sum of their money = 3500

So, a + a/2 + a/4 = 3500 

a = 2000

So, third person will get = a = Rs 2000

The second person will get = a/2 = Rs 1000

The first person will get = a/4 = Rs 500

Hence, the first, second and third person will get Rs 500, Rs 1000 and Rs 2000 respectively

Question 27. After a 20% hike, the cost of Chinese Vase is Rs 2000. What was the original price of the object?

Solution:

Let a be the original price of vase

Hike in the price of Vase = 20 %

So, price after hike will be a × (100+20)/100

So, 2000 = 12a/10

a = Rs 1666.67

Hence, the original price of the vase is Rs 1666.67