Ratio & Proportion — Multiple Choice Questions

The ratio 108 : 135 in its simplest form is

1. 23 : 27

2. 27 : 25

3. 3 : 5

4. 4 : 5

Answer

H.C.F. of 108 and 135 is 27.

$\dfrac{108 \div 27}{135 \div 27} = \dfrac{4}{5} = 4 : 5$

Hence, option 4 is the correct option.

If 30 : 42 :: 55 : x, then the value of x is

1. 95

2. 77

3. 114

4. 38

Answer

In a proportion, product of extremes = product of means.

$\Rightarrow 30 \times x = 42 \times 55\\[1em] \Rightarrow x = \dfrac{42 \times 55}{30} \\[1em] = \dfrac{2310}{30} \\[1em] = 77$

Hence, option 2 is the correct option.

If 30 : 42 :: 55 : x, then the value of x is

1. 77

2. 66

3. 88

4. 35

Answer

In a proportion, product of extremes = product of means.

$\Rightarrow 30 \times x = 42 \times 55\\[1em] \Rightarrow x = \dfrac{42 \times 55}{30} \\[1em] = \dfrac{2310}{30} \\[1em] = 77$

Hence, option 1 is the correct option.

If 7 : 9 :: x : 63, then the value of x is

1. 42

2. 49

3. 35

4. 56

Answer

In a proportion, product of extremes = product of means.

$\Rightarrow 7 \times 63 = 9 \times x\\[1em] \Rightarrow x = \dfrac{7 \times 63}{9} \\[1em] = \dfrac{441}{9} \\[1em] = 49$

Hence, option 2 is the correct option.

If a : b :: c : d, then

1. ac = bd

2. ab = cd

3. ad = bc

4. none of these

Answer

If a : b :: c : d, then the product of extremes is equal to the product of means.

Here a and d are the extremes and b and c are the means.

So, ad = bc.

Hence, option 3 is the correct option.

504 is divided into two parts in the ratio 5 : 7. The larger number is

1. 210

2. 294

3. 395

4. none of these

Answer

Sum of ratio terms = 5 + 7 = 12.

Larger number = $504 \times \dfrac{7}{12}$ = 7 × 42 = 294.

Hence, option 2 is the correct option.

₹1,520 is divided between A and B in the ratio 8 : 11. Then, A's share is

1. ₹880

2. ₹720

3. ₹640

4. ₹560

Answer

Sum of ratio terms = 8 + 11 = 19.

A's share = $1{,}520 \times \dfrac{8}{19}$ = 8 × ₹80 = ₹640.

Hence, option 3 is the correct option.

The ratio of boys and girls in a school is 13 : 8. If the number of girls is 840, the total strength of the school is

1. 1365

2. 2730

3. 2205

4. 1820

Answer

Sum of ratio terms = 13 + 8 = 21.

So, the girls form $\dfrac{8}{21}$ of the total strength.

Total strength $\times \dfrac{8}{21}$ = 840

Total strength = $840 \times \dfrac{21}{8}$ = 105 × 21 = 2205.

Hence, option 3 is the correct option.

The sides of a triangle are in the ratio 1 : 3 : 5 and its perimeter is 90 cm. The length of its largest side is

1. 36 cm

2. 40 cm

3. 50 cm

4. 54 cm

Answer

Sum of ratio terms = 1 + 3 + 5 = 9.

Largest side = $90 \times \dfrac{5}{9}$ = 5 × 10 cm = 50 cm.

Hence, option 3 is the correct option.

To reduce a ratio a : b to its simplest form, we divide each one of a and b by

1. the HCF of a and b

2. the LCM of a and b

3. ab

4. none of these

Answer

A ratio a : b is in its simplest form when the H.C.F. of a and b is 1. To reduce it, we divide each of its terms by the H.C.F. of a and b.

Hence, option 1 is the correct option.