## ML Aggarwal Class 7 ICSE Maths Model Question Paper 2

(Based on Chapters 4 to 7)

**Time allowed: 1 Hour**

**Maximum Marks: 25**

**Instructions**

- Questions 1-2 carry 1 mark each
- Questions 3-5 carry 2 marks each
- Questions 6-8 carry 3 marks each
- Questions 9-10 carry 4 marks each.

Choose the correct answer from the given four options (1-2):

Question 1.

The expression \(\left( \frac { 1 }{ 3 } \right) ^{ 9 }\) × (3^{4})^{2} is equal to

(a) 3^{9}

(b) 3

(c) \(\left( \frac { 1 }{ 3 } \right) ^{ 2 }\)

(d) \(\frac { 1 }{ 3 }\)

Solution:

Question 2.

On selling an article for ₹ 100, Renu gains ₹ 20. Her gain percentage is

(a) 25%

(b) 20%

(c) 16\(\frac { 2 }{ 3 }\) %

(d) 15%

Solution:

S.P. of an article = ₹ 100

Gain = ₹ 20

Cost Price = S.P. – Gain = ₹ 100 – ₹ 20 = ₹ 80

Question 3.

Ravi donated ₹ 3^{6} to a blind school and Rashmi donated ₹ 6^{3} to an orphanage. Who donated more money?

Solution:

Ravi donates to blind school = ₹ 3^{6} = ₹ 3 × 3 × 3 × 3 × 3 × 3 = ₹ 729

and Rashmi donates = ₹ 6^{3} = ₹ 6 × 6 × 6 = ₹ 216

Ravi donates more.

Question 4.

Find the cardinal number of the set A where A = {x | x is a two-digit number, the sum of whose digits is 11}.

Solution:

A = {x | x is a two digit number, sum of whose digits is 11}

= {29, 38, 47, 56, 65, 74, 83, 92}

n(A) = 8

Question 5.

Find the fourth proportional to 8, 24, 25.

Solution:

Fourth proportional to 8, 24, 25 = \(\frac { 24\times 25 }{ 8 }\) = 75

Question 6.

Solution:

Question 7.

18% of the apples in a basket go bad. If there are 123 good apples in the basket, find the total number of apples in the basket.

Solution:

In a basket apples go bad = 18%

Good apples = 100 – 18 = 82%

82% of total number of apples = 123

Total number of apples = \(\frac { 123\times 100 }{ 82 }\) = 150 apples

Question 8.

A natural number has been divided into two parts in the ratio 8 : 5. If the difference of two parts is 24, find the number and the two parts.

Solution:

Ratio in two parts = 8 : 5

Let first part = 8x

Then, second part = 5x

8x – 5x = 24

⇒ 3x = 24

⇒ x = \(\frac { 24 }{ 3 }\) = 8

First part = 8 × 8 = 64

and second part = 5 × 8 = 40

and number = 64 + 40 = 104

Question 9.

If 2.5 kg of apples cost ₹ 187.5, then how much quantity of apples can be bought for ₹ 330?

Solution:

Cost of 2.5 kg of apples = ₹ 187.5

Let x kg of apple can be bought for ₹ 330

187.5 : 330 = 2.5 : x

Question 10.

What sum of money will amount to ₹ 2875 in 3 years at 5% per annum simple interest?

Solution:

Amount (A) = ₹ 2875

Rate (R) = 5% p.a.

Time (T) = 3 years

Let principal = ₹ 100

Then, S.I. = \(\frac { PRT }{ 100 }\)

= \(\frac { 100\times 5\times 3 }{ 100 }\)

= ₹ 15

Then, amount = P + S.I. = ₹ 100 + 15 = ₹ 15

If amount is ₹ 115, then principal = ₹ 100

If amount is ₹ 7875 then principal

= ₹ \(\frac { 100\times 2875 }{ 115 }\)

= ₹100 × 25

= ₹ 2500