Question Detail

find the number, If 50 is subtracted from two-third of number, the result is equal to sum of 40 and one-fourth of that number.

Answer: Option B

Explanation:

Let the number is x,

$\begin{aligned} => \frac{2}{3}x-50 = \frac{1}{4}x + 40 \end{aligned}$

$\begin{aligned} <=> \frac{2}{3}x-\frac{1}{4}x = 90 \end{aligned}$

$\begin{aligned} <=> \frac{5x}{12} = 90 \end{aligned}$

$\begin{aligned} <=> x = 216 \end{aligned}$

1. Two numbers differ by 5. If their product is 336, then sum of two number is

Answer: Option D

Explanation:

Friends you remember,

$\begin{aligned} => (x+y)^2 = (x-y)^2 + 4xy \end{aligned}$

$\begin{aligned} => (x+y)^2 = (5)^2 + 4(336) \end{aligned}$

$\begin{aligned} => (x+y) = \sqrt{1369} = 37 \end{aligned}$

2. The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is

Answer: Option B

Explanation:

Let the numbers be a, b and c.
Then,

$\begin{aligned} a^2 + b^2 + c^2 = 138 \end{aligned}$
and (ab + bc + ca) = 131

$\begin{aligned} (a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca) \end{aligned}$
= 138 + 2 x 131 = 400

$\begin{aligned} => (a + b + c) = \sqrt{400} = 20. \end{aligned}$

3. The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is

Answer: Option B

Explanation:

We know

$\begin{aligned} (x + y)^2 = x^2 + y^2 + 2xy \end{aligned}$

$\begin{aligned} => (x + y)^2 = 289 + 2(120) \end{aligned}$

$\begin{aligned} => (x + y) = \sqrt{529} = 23 \end{aligned}$

4. Find the number which when multiplied by 15 is increased by 196

Answer: Option C

Explanation:

Let the number be x.
Then, 15x = x + 196
=› 14 x= 196
=› x = 14.

5. A father is twice as old as his son. 20 years ago, the age of the father was 12 times the age of the son. The present age of the father (in years) is

Answer: Option C

Explanation:

Let sons age = x. Then, fathers age = 2x.
12(x—2O) = (2x - 20) so x = 22
Fathers present age = 44 years

Question Detail

find the number, If 50 is subtracted from two-third of number, the result is equal to sum of 40 and one-fourth of that number.

1. Two numbers differ by 5. If their product is 336, then sum of two number is

2. The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is

3. The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is

4. Find the number which when multiplied by 15 is increased by 196

5. A father is twice as old as his son. 20 years ago, the age of the father was 12 times the age of the son. The present age of the father (in years) is

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Question Detail

find the number, If 50 is subtracted from two-third of number, the result is equal to sum of 40 and one-fourth of that number.

1. Two numbers differ by 5. If their product is 336, then sum of two number is

2. The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is

3. The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is

4. Find the number which when multiplied by 15 is increased by 196

5. A father is twice as old as his son. 20 years ago, the age of the father was 12 times the age of the son. The present age of the father (in years) is

Thanks ! Your comment will be approved shortly !

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