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Q:

Find the number of triangles in the given figure?

A) 10	B) 12
C) 14	D) 16

Answer & Explanation Answer: C) 14

Explanation:

The figure may be labelled as shown

The simplest triangles are ABJ, ACJ, BDH, DHF, CIE and GIE i.e 6 in number.

The triangles composed of two components each are ABC, BDF, CEG, BHJ, JHK, JKI and CJI i.e 7 in number.

There is only one triangle JHI which is composed of four components.

Thus, there are 6 + 7 + 1 = 14 triangles in the given figure.

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Q:

Find the number of triangles in the given figure?

A) 11	B) 13
C) 15	D) 17

Answer & Explanation Answer: C) 15

Explanation:

We may label the figure as shown.

The Simplest triangles are AFB, FEB, EBC, DEC, DFB and AFD i.e 6 in number.

The triangles composed of two components each are AEB, FBC, DFC, ADE, DBE and ABD i.e 6 in number.

The triangles composed of three components each are ADC and ABC i.e 2 in number.

There is only one triangle i.e DBC which is composed of four components.

Thus, there are 6 + 6 + 2 + 1 = 15 triangles in the figure

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Q:

What is the number of rectangles in the following figure?

A) 6	B) 7
C) 9	D) 11

Answer & Explanation Answer: C) 9

Explanation:

The simplest rectangles are AEHG, EFJH, FBKJ, JKCL and GILD i.e 5 in number.

The rectangles composed of two components each are AFJG and FBCL i.e 2 in number

Only one rectangle namely AFLD is composed of three components and only one rectangle namely ABCD is composed of five components.

Thus, there are 5 + 2 + 1 + 1 = 9 rectangles in the given figure.

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Filed Under: Analytical Reasoning

Q:

Ten years ago, A was half of B in age. If the ratio of their present ages is 3:4, then what will be the total of their present ages?

Answer

Let A's age 10 years ago be x years . Then B's age 10 years ago be 2x years

$\Rightarrow \frac{x+10}{2x+10}=\frac{3}{4}$

$\Rightarrow4(x+10)=3(2x+10)$

$\Rightarrow x=5$

$\therefore$ Total of their present ages = x + 10 + 2x + 10

= 3x+20

= 3 * 5 + 20 = 35 years

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Subject: Problems on Ages

Q:

The ratio of the father's age to the son's age is 3 : 1. The product of their ages is 147. The ratio of their ages after 5 years will be?

Answer

Let father's age be 3x and son's age be x years

$\Rightarrow 3x\times x=147$

$\Rightarrow x^{2}=49\Rightarrow x=7$

Father's age after 5 years = 3x + 5 = 26 years

Son's age after 5 years = x + 5 = 12 years

$\therefore$ Ratio of father's and son's ages = 26 : 12 = 13 : 6

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Subject: Problems on Ages

Q:

The average age of a couple was 26 years at the time of marriage. After 11 years of marriage, the average age of the family with 3 children become 19 years. The average age of the children is

Answer

The average age of a couple = 26 years.

Total age of couples = 26 x 2 = 52 years

$\therefore$ Total age of couple after 11 years = (52 + 2 * 11 ) = 74 years

Suppose average age of 3 children after 11 years is 3x years.

$\Rightarrow \frac{74+3x}{5}=19 \Rightarrow x=7$

The average age of children is 7 years.

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Subject: Problems on Ages

Q:

The average age of a group of 10 students is 15 years. When 5 more students join the group, the average age increase by 1 year. The average age of the new student is?

Answer

Total age of 10 students = 150 years

Total age of 15 students = 240 years

Total age of 5 new students = 240 - 150 = 90 years

$\therefore$ Average age of 5 new students = 90/5 = 18 years.

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Subject: Problems on Ages

Q:

8 years ago Ramana's mother was five times older than her daughter. After 8 years the mother will be twice older than her daughter. Find the present age of Ramana?

Answer

Let Ramana's age 8 years ago be x years and mother's age 8 years ago be 5x

$\Rightarrow$ 2(x + 16) = 5x + 16