Competitive Exams : PYQ Practice 1

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Competitive Exams : PYQ Practice : Click Here

Q. A pouch contains a total of ₹150 in which 25 paise, 10 paise and 5 paise coins are in the ratio 1 : 2 : 3. How many 10-paise coins are there ?

(A) 100  (B) 200  (C) 207  (D) 500

Solution

Let the numbers of coins be: $$\text{x, 2x, 3x}$$

for 25p, 10p and 5p coins respectively.

Formula : $$\text{Total Value }=\sum (\text{Number of coins }\times \text{Value of each coin})$$

Convert ₹150 into paise: $$₹150=15000\text{ paise}$$

Therefore,

$$\text{25x + 10(2x) + 5(3x) = 15000}$$

$$\text{25x + 20x + 15x = 15000}$$

$$\text{60x = 15000}$$

$$\text{x = 250}$$

Number of 10-paise coins: $$\text{2x = 2 × 250 = 500}$$

Ans: (D) 500

​Trick:

$$\text{25(1) + 10(2) + 5(3) = 60}$$

$$\text{15000 ÷ 60 = 250}$$

10-paise coins: $$\text{2 × 250 = 500}$$

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Q. A pouch contains a total of ₹864. It includes ₹1, 50-paise and 25-paise coins in the ratio 2 : 3 : 4. What is the number of 25-paise coins ?

(A) 500  (B) 716  (C) 768  (D) None

Solution

Let the number of ₹1, 50p and 25p coins be: $$2x,3x,4x$$

Formula: $$\text{Total Value }=\sum (\text{Number of coins }\times \text{Value of each coin})$$

Convert ₹864 into paise: $$₹864=86400\text{ paise}$$

Therefore,

$$\text{2x(100) + 3x(50) + 4x(25) = 86400}$$

$$\text{200x + 150x + 100x = 86400}$$

$$\text{450x = 86400}$$

$$\text{x = 192}$$

Number of 25-paise coins: $$\text{4x = 4×192 = 768}$$

Ans: (C) 768

​Trick:

Value of one ratio group:

$$\text{2(₹1) + 3(₹0.50) + 4(₹0.25) = 2 + 1.5 + 1 = ₹4.5}$$

$$\text{864 ÷ 4.5 = 192}$$

25p coins: $$\text{4 × 192 = 768}$$

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Q. If A : B = 3 : 4 and B : C = 1 : 2, then find A : B : C.

Options: A. 3 : 4 : 8   B. 1 : 3 : 4   C. 4 : 3 : 2   D. 1 : 2 : 4

Solution

Given: $$\text{A:B = 3:4 B:C = 1:2}$$

Make B equal.

In the first ratio, B = 4.
In the second ratio, B = 1.

Multiply the second ratio by 4:

$$\text{B:C = 4:8}$$

Therefore: $$\text{A:B:C = 3:4:8}$$

Ans: A. 3 : 4 : 8

Trick

$$\text{A:B = 3:4, B:C = 1:2}$$

Since $1\times 4=4$,

$$\text{A : B : C = 3 : 4 : 8}$$

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Q. Find the mean proportional between 144 and 225.

(A) 135  (B) 180  (C) 250  (D) 200

Trick:

If a and b are two numbers, their mean proportional is: √$$\text{a×b}$$

So,

$$\text{x = √144×225 = √12×12×15×15 = 12×15 = 180}$$

Ans: (B) 180

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Q. If (3A = 2B = 5C), then find (A : B).

A) 10 : 15 : 6   B) 6 : 15 : 5  C) 12 : 4 : 15  D) 9 : 10 : 12

Solution

Given: 3A = 2B = 5C

 Let the common value be k.

Then:

A = k/3, B = k/2, C = k/5

So,

A : B : C = 1/3 : 1/2 : 1/5

Take LCM of 3, 2, 5 = 30:

A : B : C = 10 : 15 : 6 

Ans: A) 10 : 15 : 6

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Fourth Proportional

Q. What is the fourth proportional of 4, 7, 16, ?

Solution

Given:

4 : 7 :: 16 : x

Using the proportion rule:

4x = 7×16

4x = 112

x = 112/4 = 28

Ans: A) 28

Short Trick: Fourth proportional (চতুৰ্থ সমানুপাতিক)= 2nd×3rd/1st = 7 × 16/4 = 28

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